Non-staggered Grid Arrangement Research Articles

Research on Effects of Obstacles on Heat Transfer and Fluid Flow in Backward Facing Step Flow

An extensive research has been done on heat transfer and pressure drop characteristics in micro-channel using liquid water. A baffle has been introduced downstream the sudden expansion zone to enhance the rate of heat transfer. The height and the location of the baffle were varied for the Reynolds number range 50≤ Re ≤ 200, which is a laminar flow. Twodimensional flow domain with non-staggered grid arrangement was taken and the two-dimensional mass, momentum and energy equation was solved using finite volume method in ANSYS 16.2. This study reports that the presence of baffle in the microchannel increased the rate of heat transfer. The skin friction coefficient has been calculated and the parameters influencing the heat transfer augmentation have been optimized

Thermal stratification studies in a side heated water pool for advanced heavy water reactor applications

Strong heat source at the isolation condenser wall of an Advanced Heavy Water Reactor, results in natural convection in gravity driven water pool, which leads to a thermally stratified pool. Governing equations simulating fluid flow and heat distribution are solved numerically by a general purpose Computational Fluid Dynamics solver developed at Indian Institute of Technology, Kanpur. Incompressible finite volume method with non-staggered grid arrangement is used in this exercise. This algorithm is fully implicit and semi-coupled. Turbulent natural convection in a boundary layer for high Rayleigh numbers is analyzed by the Lam–Bremhorst k − e turbulence model. Analysis of unsteady laminar natural convection in a side-heated water cavity is also done for different values of Rayleigh number. Results show a warm fluid layer floating on the top of gradually colder layer (along the vertical direction) that indicates the presence of thermal stratification phenomenon. This fact necessitates additional safety features in such a system so that the detrimental effect such as stratification is minimized.

Comparison of trust-region-based and evolutionary methods for optimization of flow geometries†

Optimization has become increasingly important in computer-aided engineering, and applications of engineering optimization to design, control, operations, and planning already exist. Since in the context of numerical flow simulation no information on the gradient information of the objective function is available, or is very difficult to obtain, in such optimization cases it is advantageous to use an optimization technique which does not directly depend on the derivative. The aim of this study is to investigate two optimization techniques, the trust-region-based method and the evolutionary algorithm technique, and compare them quantitatively with respect to efficiency, quality, and working strategy. A tool based on free-form deformation (FFD) is employed for the variation of flow geometry. This simulation tool is the parallel multigrid flow solver FASTEST, which uses a fully conservative finite-volume method for solving the incompressible Navier–Stokes equations on a non-staggered cell-centred grid arrangement. The optimization tools are investigated by considering the optimization of the connection of two pipes with respect to the minimization of the pressure drop. This problem can be considered as a representative test case for a practical three-dimensional flow configuration. †This is an extended and enhanced version of work presented at the mini-symposium on Evolutionary Algorithms: Recent Applications in Engineering and Science organized by Dr William Annicchiarico at the 7th World Congress on Computational Mechanics, Los Angeles, July 2006.

Heat transfer due to double laminar slot jets impingement onto an isothermal wall within one side closed long duct

In this study, heat transfer due to double impinging vertical slot jets onto an isothermal wall was investigated numerically for laminar flow regime. Navier–Stokes and energy equations were discretized with a finite volume procedure on a non-staggered grid arrangement using SIMPLEM (SIMPLE-Modified) algorithm. The effect of the jet Reynolds number, the jet-isothermal bottom wall spacing, and the distance between two jets on heat transfer and flow field was examined. Air was chosen as the working fluid (Pr=0.71). It is found that multi-cellular flow is formed in the impingement region due to interaction between two jets and entrainment effects in the duct. The mean Nusselt number increases almost linearly with increasing of Reynolds number at isothermal surface. When Reynolds number of the first jet is higher than second one the heat transfer is enhanced significantly.

Flow over a bluff body from moderate to high Reynolds numbers using large eddy simulation

Large eddy simulation (LES) is performed to study the uniform approach flow over a square-section cylinder with different Reynolds numbers, ranging from 10 3 to 5 × 10 6. Two different sub-grid scale models, the Smagorinsky and a dynamic one-equation model, are employed. An incompressible finite-volume code, based on a non-staggered grid arrangement and an implicit fractional step method with second-order accuracy in space and time, is used. The structure of the flow is studied with the instantaneous and the mean quantities such as pressure, turbulent stresses, turbulent kinetic energy, vorticity, the second invariant of velocity gradient and streamlines. The Strouhal number, the mean and RMS values of the lift and drag are computed for various Reynolds numbers, which show a good agreement with the available experimental results. It is found that the effect of Reynolds number on the global quantities, the mean and the large scale instantaneous flow-structures is not much at the higher Reynolds numbers, i.e. Re > 2 × 10 4. In this range of Reynolds numbers, the small scales of the instantaneous structures are more complex and chaotic as they compare with the larger ones.

Numerical study of flow and heat transfer in curvilinear ducts: applications of elliptic grid generation

A numerical study was performed to investigate heat transfer and fluid flow in curvilinear shaped duct geometries. SIMPLEM algorithm was used with a non-staggered grid arrangement to solve Navier–Stokes and energy equations in curvilinear coordinates. To obtain grid generation for curvilinear surfaces elliptic grid generation method was used. Two examples were demonstrated for laminar flow regime in the study: First, asymmetric sinusoidal wavy walled duct and second partially inclined duct geometry were chosen. The results show that SIMPLEM algorithm with non-staggered grid arrangement is a useful technique to solve temperature and flow field in curvilinear ducts by using elliptic grid generation method.

Comparison of position of a heated thin plate located in a cavity for natural convection

In this numerical study, natural convection heat transfer in a square cavity with a heated plate built-in vertically and horizontally was investigated. In order to obtain finite difference equations, transport and energy equations were integrated based a finite control volume with non-staggered grid arrangement. The discretized equations were solved with TDMA using SIMPLEM algorithm iteratively. The study was performed for different Rayleigh number values ranging from 10 4 to 10 6 and for different aspect ratios and position of heated plate. Air was chosen as a working fluid (Pr=0.71). The effect of the position and aspect ratio of heated plate on heat transfer and flow were addressed

Numerical Analysis of Unsteady Conjugate Heat Transfer and Thermal Stress for a Curved Piping System Subjected to Thermal Stratification

This paper addresses three-dimensional numerical analyses of the unsteady conjugate heat transfer and thermal stress for a PWR pressurizer surge line pipe with a finite wall thickness, subjected to internally thermal stratification. A primary emphasis of the present study is placed on the investigation of the effects of surge flow direction on the determinations of the transient temperature and thermal stress distributions in the pipe wall. In the present numerical analysis, the thermally stratified flows (in-surge flow and out-surge flow) in the pipe line are simulated using the standard κ−ε turbulent model and a simple and convenient numerical method of treating the unsteady conjugate heat transfer on a non-orthogonal coordinate system is developed. The unsteady conjugate heat transfer analysis method is implemented in a finite volume thermal-hydraulic computer code based on a non-staggered grid arrangement, SIMPLEC algorithm and higher-order bounded convection scheme. The finite element method is employed for the thermal stress analysis to calculate non-dimensional stress distributions at the piping wall as a function of time. Some numerical calculations are performed for a PWR pressurizer surge line pipe model with shortened length, subjected to internally thermal stratification caused either by insurge or outsurge flow with a specified velocity, and the results are discussed in detail.

Numerical simulation of scour by a free falling jet

In this paper the numerical simulation of scour by a free falling jet is presented. It is assumed that the flow is two-dimensional, the alluvium is cohesionless, and that at the beginning of a run, i.e. at t = 0, the movable bed is flat. The scour simulation involves three basic steps: simulation of a turbulent flow in the stilling basin of a free falling jet, determination of distribution of sand concentration, and computation of bed deformation. The flow simulation rests on the momentum equations, the continuity equation, and on the k-ε equations for turbulent flows. A general 2-D non-orthogonal curvilinear computational domain is used; the solution is by the finite volume method, with a non-staggered grid arrangement. The SIMPLE scheme is used for pressure correction and the checkerboard problem is solved with a momentum interpolation scheme. The distribution of sand concentration is determined on the basis of the convection-diffusion equation. An appropriate boundary condition for concentration at the bed, which takes into account the effect of bed-load, is implemented. The bed deformation is computed with the aid of the sediment continuity equation. The aforementioned steps are repeated until the equilibrium bed surface (i.e. the equilibrium scour hole) is reached. The results of the numerical simulation appear to compare favourably with experiment.

SIMULTANEOUS NATURAL-CONVECTION HEAT TRANSFER ABOVE AND BELOW AN ISOTHERMAL HORIZONTAL THIN PLATE

Numerical studies were conducted to investigate the simultaneous natural-convection heat transfer above and below an isothermal thin plate in an infinite space. The full two-dimensional conservation equations for laminar flows were solved. The numerical approach was based on the finite-volume technique with a nonstaggered grid arrangement. The SIMPLE algorithm was used for handling the pressure-velocity coupling. Plate width and temperature were used to vary the Rayleigh number over the range 1.0 2 10 5 to 1.7 2 10 7 . The expressions for numerical local and average Nusselt number were correlated, and horizontal velocity and temperature profiles were provided. It was found that the upper-surface Nusselt numbers are smaller than the corresponding lower-surface Nusselt numbers. Numerical results for upward- and downward-facing isothermal horizontal plates (single-sided heat transfer) were also shown for comparison. For these cases, Nusselt numbers on the upward-facing surface are larger than those on the downward-facing surface.

Simulation of fluid flow in granular microstructure using a non-staggered grid scheme

A finite difference numerical scheme has been utilized to simulate fluid flow in granular microstructures. The pixels of their digital images represent the granular microstructure in the finite difference grid. The scheme utilizes a non-staggered grid arrangement, which requires only one finite difference mesh to solve the governing fluid flow equations. As such, the scheme is more efficient when it comes to dealing with non-orthogonal coordinates and complex geometry of boundary conditions such as that of granular microstructure. The numerical scheme is verified by comparing the permeability values of a medium of packed columns to a closed form solution. It is then used to evaluate the permeability coefficients of idealized and natural granular microstructures. It has been found that as the directional aspect ratio increases, the resistance of a particle to fluid flow increases, which results in a decrease in the permeability coefficient. A medium of elliptical particles has higher permeability coefficient than a medium of rectangular particles for the same porosity because of its lower surface area. The permeability anisotropy has been found to increase with an increase in the aspect ratio or a decrease in porosity. Spherical glass beads have been found to have higher permeability coefficients than Ottawa sand and Silica.

Numerical study of simultaneous natural convection heat transfer from both surfaces of a uniformly heated thin plate with arbitrary inclination

Numerical studies were conducted to investigate the natural convection heat transfer around a uniformly heated thin plate with arbitrary inclination in an infinite space. The numerical approach was based on the finite volume technique with a nonstaggered grid arrangement. For handling the pressure–velocity coupling the SIMPLE-algorithm was used. QUICK scheme and first order upwind scheme were employed for discretization of the momentum and energy convective terms respectively. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 4.8×106 to 1.87×108. Local and average heat transfer characteristics were compared with regarding to the inclination angle. The empirical expressions for local and average Nusselt number were correlated. It has been found that for inclination angle less than 10∘, the flow and heat transfer characteristics are complicated and the average Nusselt number can not be correlated by one equation while for inclination angle larger than 10∘, the average Nusselt number can be correlated into an elegant correlation.

Natural convection heat transfer by heated partitions within enclosure

In this study, natural convection heat transfer and fluid flow of two heated partitions. within an enclosure have been analysed numerically. The right side wall and the bottom wall of the enclosure were insulated perfectly while the left side wall and top wall were maintained at the same uniform temperature. The partitions were placed on the bottom of the enclosure and their temperatures were kept higher than the non-isolated walls. The effects of position and heights of the partitions on heat transfer and flow field have been investigated. Computations for Rayleigh number in the range of 10 4 and 10 6 have been conducted. Using the control volume approach, finite difference equations are obtained with non-staggered grid arrangement, a computer program based on the SIMPLEM algorithm was developed. The finite difference equations were solved iteratively with a line-by-line Thomas algorithm.

Numerical Analysis of Thermal Stratification in a Circular Pipe

This paper presents an effective numerical method for predicting the stratified flow in a horizontal circular pipe. The method employs a body-fitted, nonorthogonal grid system to accommodate the pipe wall of circular geometry and the interface of the two fluids at different temperatures, of which the level is variable. The transient behaviors of fluid flow and temperature distribution in the piping are simulated using the finite volume approach. The convection term is approximated by a higher-order bounded scheme named HLPA, which is known as a high-resolution and bounded discretization scheme. The cell-centered, nonstaggered grid arrangement is adopted and the resulting checkerboard pressure oscillation is prevented by the application of modified momentum interpolation scheme. The SIMPLE algorithm is employed for the pressure and velocity coupling. The new way of treating the unsteady conjugate heat transfer problem is presented. The present method has been applied to the stratified flow in the pressurizer surge line of the nuclear reactor, and the results have been discussed. In addition, this study has investigated the effects of level of the interface between the two stratified fluids on the transient evolution of temperature distributions in the piping wall.

EFFECT OF INCLINED VORTEX GENERATORS ON HEAT TRANSFER ENHANCEMENT IN A THREE-DIMENSIONAL CHANNEL

Three-dimensional unsteady flow and heat transfer in a channel with inclined block shape vortex generators mounted on one side of a channel flow are investigated for different Reynolds numbers, Re H= 400 - 1500 , and Pr = 0.71. This study was informed to gain an understanding of the flow phenomena and calculate the heat transfer and pressure drop for different Reynolds numbers. The effect of computational domain, angle of incidence, size of the vortex generator, and the discretization schemes on the results are also investigated. Simulations use an incompressible finite volume code, based on a fractional step technique with a multigrid pressure Poisson solver and a nonstaggered grid arrangement.

EFFECT OF INCLINED VORTEX GENERATORS ON HEAT TRANSFER ENHANCEMENT IN A THREE-DIMENSIONAL CHANNEL

Three-dimensional unsteady flow and heat transfer in a channel with inclined block shape vortex generators mounted on one side of a channel flow are investigated for different Reynolds numbers, Re H= 400 - 1500 , and Pr = 0.71. This study was informed to gain an understanding of the flow phenomena and calculate the heat transfer and pressure drop for different Reynolds numbers. The effect of computational domain, angle of incidence, size of the vortex generator, and the discretization schemes on the results are also investigated. Simulations use an incompressible finite volume code, based on a fractional step technique with a multigrid pressure Poisson solver and a nonstaggered grid arrangement.

DIRECT NUMERICAL SIMULATION OF BLUFF BODY FLOWS USING NON-STAGGERED GRIDS

The present authors pointed out in the previous paper [1] that the implicit SMAC scheme is quite efficient and non-staggered grid arrangement can decrease the computational effort and save the storage memory which is very important to the direct numerical simulation (DNS) of complicated 3-D flow fields. But using non-staggered grid arrangement, the pressure field oscillation (PFO) ordinarily occurs and also, the pressure on the solid walls including sharp corners need to be prescribed directly as the pressure boundary conditions. In this paper, a new interpolation method, which is a modification to Cheng and Armfield's interpolation formulation, is presented in order to completely prevent PFO from occurring, Moreover, a more accurate specification method of wall pressures and special treatment of pressures at sharp corners are proposed. To test the new methods proposed, the DNS of flow past a square cylinder and flows over backward-facing steps, which are typical of the flow fields with sharp corners, is made using the implicit SMAC scheme combined with these methods. The calculated results are compared with the previous experimental and numerical data and show good agreement with them.

Improved Modeling of Turbulent Forced Convective Heat Transfer in Straight Ducts

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in their fully developed state at low Reynolds number. The authors have developed a low Reynolds number version of the nonlinear k-ε model combined with the heat flux models of simple eddy diffusivity (SED), low Reynolds number version of generalized gradient diffusion hypothesis (GGDH), and wealth ∝ earning × time (WET) in general three-dimensional geometries. The numerical approach is based on the finite volume technique with a nonstaggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with the nonlinear k-ε model, combined with the Lam-Bremhorst and the Abe-Kondoh-Nagano damping functions for low Reynolds numbers.

An overlapping control volume method for the Navier-Stokes equations on non-staggered grids

An algorithm, based on the overlapping control volume (OCV) method, for the solution of the steady and unsteady two-dimensional incompressible Navier-Stokes equations in complex geometry is presented. The primitive variable formulation is solved on a non-staggered grid arrangement. The problem of pressure-velocity decoupling is circumvented by using momentum interpolation. The accuracy and effectiveness of the method is established by solving five steady state and one unsteady test problems. The numerical solutions obtained using the technique are in good agreement with the analytical and benchmark solutions available in the literature. On uniform grids, the method gives second-order accuracy for both diffusion- and convection-dominated flows. There is little loss of accuracy on grids that are moderately non-orthogonal

Performance of RNG Turbulence Modelling for Forced Convective Heat Transfer in Ducts

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in straight ducts using the RNG (Re-Normalized Group) turbulence method. A computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts with different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with the RNG κ−ϵ model and the RNG non-linear κ-ϵ model of Speziale. The turbulent heat fluxes are modeled by the simple eddy diffusivity (SED) concept, GGDH and WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models arc implemented for an arbitrary three dimensional duct. Fully developed condition is achieved by imposing cyclic boundary conditions in the main flow direction. The numerical approach is based on the finite volume technique with a non-staggered grid arrangement. The pressure-velocity coupling is handled by using the SIMPLEC-algorithm. The convective terms are treated by the QUICK, scheme while the diffusive terms are handled by the central-difference scheme. The hybrid scheme is used for solving the κ and ϵ equations. The overall comparison between the models is presented in terms of friction factor and Nusselt number. The secondary flow generation is also of major concern.