A novel multiphase DNS approach for handling solid particles in a rarefied gas

A comprehensive model is proposed for multiphase DNS simulations of gas–solid systems involving particles of size comparable to the mean free path of the gas and to that of the bounding geometry. The model can be implemented into any multiphase Direct Numerical Simulation (DNS) method. In the current work, the Volume of Fluid (VOF) method is used, and it is extended to allow for the incorporation of rarefaction effects. For unbounded flow, the model is in excellent agreement with experimental data from the literature. For flows in closed conduits, the model outperforms the alternate approach of using a slip boundary condition at the particle surface for the most relevant degrees of rarefaction and confinement. The proposed model is also able to correctly handle particle–particle interception. The model is intended for low particle Reynolds number flows, and can be applied to resolve in great detail phenomena in a large number of industrial applications (such as filtration of fine particles in porous media).     

Non-conservative pressure-based compressible formulation for multiphase flows with heat and mass transfer

A pressure-based compressible multiphase flow solver has been developed based on non-conservative discretization of the mixture continuity equation. The formulation is an extension of the single phase incompressible pressure-correction approach, such that it can be applied to both two-phase flows using interface resolving methods and general n-phase ensemble-averaged mixture flows. The formulation is currently presented with the single pressure and single temperature assumption, but extension to multiple temperatures is straightforward. A robust treatment of phase change allows the method to model conditions with rapid phase change such as expansion through nozzles and valves. The method has been validated thoroughly using canonical single phase problems such as the shock tube, tank filling and sudden valve closure problems. Multiphase flow validation has been carried out for sound propagation in mixtures using the ensemble-averaged model and pressure wave transmission and reflection across an air-water interface, using the level set interface tracking method. The method has been used to study sound propagation in saturated steam-water systems under thermodynamic non-equilibrium, where the expected drastic reduction in the speed of sound is reproduced. Finally the method is applied to the problem of critical (choked) flow in a nozzle for a saturated steam-water system.     

DNS of turbulent heat transfer in a channel flow with a high spatial resolution

Direct numerical simulations of turbulent heat transfer in a channel flow are performed to investigate the effects of Reynolds and Prandtl numbers on higher-order turbulence statistics such as a turbulent Prandtl number and the budget for the dissipation rate of the temperature variance. The Reynolds numbers based on the friction velocity and the channel half width are 180 and 395, and the molecular Prandtl numbers Pr’s 0.71–10.0. Careful attention is paid to ensure accuracy of the higher-order statistics through the use of a high spatial resolution comparable to Batchelor length scale. The wall-asymptotic value of the turbulent Prandtl number is mostly independent of Reynolds number for the current range of Pr’s. The budget for the dissipation rate of the temperature variance has been computed, and the negligible effect of a Reynolds number on the sum of all source and sink terms in near-wall region in the current computational range is found. This result is quite similar to the one in the budget for the dissipation rate of turbulent energy. In addition, a priori test for existing models is also performed to assess the Pr dependence on the individual terms and their summations in the budget.     

Perturbation method for heat exchange between a gas and solid particles

The analytical perturbation method is applied here to solve the problem of radiative heat transfer between a gas and solid particles. The data obtained are compared with results calculated by the numerical Runge-Kutta method.     

Heat transfer characteristics of a vertical porous heat storage saturated by a liquid and spherical solid particles

A fundamental study on the transient characteristics of a vertical rectangular porous heat storage, which was composed of a fluid (liquid) and spherical solid particles, has been numerically carried out under one vertical wall exposed to a constantheat-flux condition while other walls thermally insulated. The present study has clarified the effects of the porosity, the heatflux as a receiving heat, thermophysical properties and the dimensions of the heat storage (aspect-ratioH/W, height to width of the rectangular cavity) on the transient characteristics of the porous heat storage proposed. It was concluded that the natural convection occurred in the heat storage had an important role in evaluating the transient heat transfer characteristics, that is, the convection occurred had contributed to shortening the time period until the quasi-steady state after starting the heating to the heat storage and to homogenizing thermally the porous heat storage. From the results obtained, it is possible to obtain optionally the time period until the quasi-steady state and the amount of the heat stored into or taken out from the porous heat storage proposed by selecting the proper combination of both phases and the dimension of the storage, in comparison with the single phase heat storage.     

Fractional order theory in thermoelastic solid with three-phase lag heat transfer

In this work, the field equations of the linear theory of thermoelasticity have been constructed in the context of a new consideration of Fourier law of heat conduction with time-fractional order and three-phase lag. A uniqueness and reciprocity theorems are proved. One-dimensional application for a half-space of elastic material in the presence of heat sources has been solved using Laplace transform and state space techniques Ezzat (Canad J Phys Rev 86:1241–1250, 2008). According to the numerical results and its graphs, conclusion about the new theory has been established.     

Settling motion of interacting solid particles in the vicinity of a plane solid boundary

The sedimentation of $N?1$ small arbitrarily-shaped solid bodies near a solid plane is addressed by discarding inertial effects and using 6N boundary-integral equations. Numerical results for 2 or 3 identical spheres reveal that combined wall–particle and particle–particle interactions deeply depend on the cluster's geometry and distance to the wall and may even cancel for a sphere which then moves as it were isolated. To cite this article: A. Sellier, C. R. Mecanique 333 (2005).     

DNS of heat transfer increase in a cylinder stagnation region due to wake-induced turbulence

Heat transfer in the stagnation point area of a heated cylinder is investigated using Direct Numerical Simulation (DNS). The heated cylinder is subjected to the turbulent wake of a smaller cylinder placed upstream. Two Reynolds numbers based on the diameter of the heated cylinder of 13,200 and 48,000 are chosen. In accordance with correlations in the literature, an increase in heat transfer compared to fully laminar flow is found for all angles along the front circumferential area of the heated cylinder. However, due to the presence of the wake, the maximum increase is shifted away from the centerline. The characteristic turbulence level and Nusselt number in the present study are an order of magnitude higher than those reported in previous simulations. The DNS results obtained, are in good agreement with an existing experimental correlation. Finally, relevant flow structures and instantaneous temperature fields are visualized.     

DNS of heat transfer in turbulent and transitional channel flow obstructed by rectangular prisms

Direct numerical simulation (DNS) of heat transfer in a channel flow obstructed by rectangular prisms has been performed for Re_τ = 80–20, where Re_τ is based on the friction velocity, the channel half width and the kinematic viscosity. The molecular Prandtl number is set to be 0.71. The flow remains unsteady down to Re_τ = 40 owing to the disturbance induced by the prism. For Re_τ = 30 and 20, the flow results in a steady laminar flow. In the vicinity of the prism, the three-dimensional complex vortices are generated and heat transfer is enhanced. The Reynolds number effect on the time-averaged vortex structure and the local Nusselt number are investigated. The mechanism of the heat transfer enhancement is discussed. In addition, the mean flow parameters such as the friction factor and the Nusselt number are examined in comparison with existing DNS and experimental data.     

Effect of inertial particles with different specific heat capacities on heat transfer in particle-laden turbulent flow

The effect of inertial particles with different specific heat on heat transfer in particle-laden turbulent channel flows is studied using the direct numerical simulation(DNS) and the Lagrangian particle tracking method. The simulation uses a two-way coupling model to consider the momentum and thermal interactions between the particles and turbulence. The study shows that the temperature fields display differences between the particle-laden flow with different specific heat particles and the particle-free flow,indicating that the particle specific heat is an important factor that affects the heat transfer process in a particle-laden flow. It is found that the heat transfer capacity of the particle-laden flow gradually increases with the increase of the particle specific heat. This is due to the positive contribution of the particle increase to the heat transfer. In addition,the Nusselt number of a particle-laden flow is compared with that of a particle-free flow.It is found that particles with a large specific heat strengthen heat transfer of turbulent flow, while those with small specific heat weaken heat transfer of turbulent flow.     

A novel transient wall heat transfer approach for the start-up of SI engines with gasoline direct injection

The introduction of CO₂-reduction technologies like Start–Stop or the Hybrid-Powertrain and the worldwide stringent emission legislation require a detailed optimization of the engine start-up. The combustion concept development as well as the calibration of the engine control unit makes an explicit thermodynamic analysis of the combustion process during the start-up necessary. Initially, the well-known thermodynamic analysis of in-cylinder pressure at stationary condition was transmitted to the highly non-stationary engine start-up. For this running mode of the engine the current models for calculation of the transient wall heat fluxes were found to be misleading. With a fraction of nearly 45% of the burned fuel energy, the wall heat is very important for the calculation of energy balance and for the combustion process analysis. Based on the measurements of transient wall heat transfer densities during the start-up presented in a former work (Lejsek and Kulzer in Investigations on the transient wall heat transfer at start-up for SI engines with gasoline direct injection. SAE Paper), the paper describes the development of adaptations to the known correlations by Woschni (MTZ 31:491, 1970), Hohenberg (Experimentelle Erfassung der Wandwärme von Kolbenmotoren. TU Graz, Habil., 1980) and Bargende (Ein Gleichungsansatz zur Berechnung der instationären Wandwärmeverluste im Hochdruckteil von Ottomotoren. TH Darmstadt, PhD-Thesis, 1991) for the application during engine start-up. To demonstrate the high accuracy of the model, the results of the cyclic resolved thermodynamic analysis using the presented novel approaches were compared with the results of the measurements. It is shown, that the novel heat flux models for the engine start-up process gives a cyclic resolved thermodynamic analysis to optimize the engine start-up pretty efficient.     

DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.     

The influence of pipe length on thermal statistics computed from DNS of turbulent heat transfer

We present results from direct numerical simulation of turbulent heat transfer in pipe flow at a bulk flow Reynolds number of 5000 and Prandtl numbers ranging from 0.025 to 2.0 in order to examine the effect of streamwise pipe length (πδ ≡ πD/2 ? L ? 12πδ) on the convergence of thermal turbulence statistics. Various lower and higher order thermal statistics such as mean temperature, rms of fluctuating temperature, turbulent heat fluxes, two-point auto and cross-correlations, skewness and flatness were computed and it is found that the value of L required for convergence of the statistics depends on the Prandtl number: larger Prandtl numbers requires comparatively shorter pipe length for convergence of most of the thermal statistics.     

The influence of pipe length on thermal statistics computed from DNS of turbulent heat transfer

We present results from direct numerical simulation of turbulent heat transfer in pipe flow at a bulk flow Reynolds number of 5000 and Prandtl numbers ranging from 0.025 to 2.0 in order to examine the effect of streamwise pipe length (πδ ≡ πD/2 ⩽ L ⩽ 12πδ) on the convergence of thermal turbulence statistics. Various lower and higher order thermal statistics such as mean temperature, rms of fluctuating temperature, turbulent heat fluxes, two-point auto and cross-correlations, skewness and flatness were computed and it is found that the value of L required for convergence of the statistics depends on the Prandtl number: larger Prandtl numbers requires comparatively shorter pipe length for convergence of most of the thermal statistics.     

State space approach to thermoelectric fluid with fractional order heat transfer

A new mathematical model for electromagnetic thermofluid equation heat transfer with thermoelectric properties using the methodology of fractional calculus is constructed. The governing coupled equations in the frame 11 of the boundary layer model are applied to variety problems. Laplace transforms and state space techniques (Ezzat Can J Phys Rev 86:1241–1250 in 2008) are used to get the solution of a thermal shock problem, a layer problem and a problem for the semi-infinite space in the presence of heat sources. According to the numerical results and its graphs, a parametric study of time-fractional order 0 < α ≤ 1, on temperature and the thermoelectric figure of merit are conducted.