A numerical analysis is made on the turbulent boundary layers with injection and suction through a slit using five different turbulence models. The five models are three eddy viscosity models (zero-, one- and two-equation models) and two different types Reynolds stress model. Published experimental data on the skin friction factor, the mean velocity profiles, and Reynolds stress profiles are used to assess the performance of the model calculations. Applicabilities of these models to the turbulent boundary layers with injection and suction are investigated. For flow with injection, the Reynolds stress model gives good agreement with the experimental data. The zero-equation model provides very accurate prediction for suction flow.
A three-dimensional temperature fluctuation analysis was carried out using a general-purpose multidimensional thermohydraulic analysis code for a 1 : 2 scale model water experiment and a 1 : 1 scale model sodium experiment simulating thermal striping phenomena. The code was incorporated with an algebraic stress turbulence model (ASM) and an adaptive control system based on the fuzzy theory to control time step sizes. Calculational results under the test conditions of various flow velocity ratios showed good agreement with the measured intensity distribution and maximum value of the temperature fluctuations. From the analysis, it was concluded that (1) the ASM is applicable to the intensity evaluation of the temperature fluctuations related to the thermal striping phenomena, (2) a combined approach of the ASM and the higher-order accurate schemes such as the quadratic upstream interpolation for convective kinematics (QUICK) and QUICK with the filtering remedy and methodology (FRAM) is recommended to analyze overall turbulent flow and temperature fields in engineering applications, and (3) the adaptive time step size control system is practical in reducing computing efforts.
To investigate the motion of fluid particles around a cylinder in turbulent flows, we developed a new model for simulating the trajectory of particles : the combined model of kinematic simulation (KS) and random flight (RF). The large-scale turbulence is simulated by a sum of random Fourier modes varying in space and time, and the small-scale turbulent fluctuation is simply modelled by an ITO type of stochastic differential equation with a memory time comparable to the Lagrangian integral time scale TLS of small-scale motion. The Lagrangian properties of fluid particles in homogeneous isotropic turbulence with uniform mean flow have been examined. Some new results have been obtained using this new model : (a) the cross-correlation of the displacements due to the large- and small-scale motions is negligibly small ; (b) random small-scale motion causes decorrelation of the large-scale velocity ; (c) the value of TLS used in RF can be reasonably estimated from pure KS.
An explicit method of lines for solving compressible Navier-Stokes equations which consists of the rational Runge-Kutta time stepping scheme and central finite differencing, is applied to compute low-speed flows in pipes with varying cross sections. Low-Reynolds-number flow in a suddenly expanding pipe is calculated as a test problem, in order to assess the forms of the basic equations in general coordinates and to confirm the accuracy of the method. The results show that the quasi-conservation law form is more reliable than the full conservation law form, and the calculated reattachment distance is in good agreement with other established results. In the following, calculations of the flows in a pipe with a valve are carried out. The results are compared with experimental results. The discharge coefficients and flow patterns for each valve lift are accurately obtained.
Capsule velocity in hydraulic and pneumatic pipelines is analyzed in its equilibrium state based on a coaxial annular flow model. The capsule is cylindrical and is assumed to move coaxially, and Coulomb friction is considered when the capsule has wheels. Properties of carrier fluid are included in a nondimensional friction parameter which consists of kinematic viscosity of fluid, density ratio, Coulomb frictional coefficient, pipe diameter and gravity acceleration. Effects of length/diameter ratio, diameter ratio and friction parameter on the capsule velocity are calculated. The maximum capsule velocity is limited by the diameter ratio. Pressure and shear forces on the capsule and a pressure drop across the capsule are also discussed, and the possibility of drag reduction due to the capsule is suggested.
Experiments were performed in a two-phase, two free-stream plane mixing layer to study the behavior of heavy spheres in an intermittent shear flow. Particles with three different diameters were employed in these experiments. Comparisons between data on streamwise and transverse components of particle and gas velocities are presented. These data, as well as flow visualization images, suggest that the ratio of the particle time constant τp and the large-scale eddy turnover time plays an important role in the cross-stream transport of a heavy dispersed phase. When the τp/τ was approximately on the order of 1, heavy particles began to move with gas flow. There exists movement of heavy spheres back toward the particle feed stream. The transverse component of large-particle turbulent velocity, vp', in the interior of the layer was observed to be significantly smaller than the corresponding streamwise component, up' <v'2>/<u'2> of the particle reaches an asymptotic value, 0.2, around the high-speed side of the mixing layer.
The entrance geometry effect on flooding was examined in vertical air-water countercurrent flow. Flooding occurred by a drastic amplification of local interfacial disturbance generally initiated at the upper or lower entry. In order to analyze the flooding phenomena, the local flow properties at these entries should be understood. The void fraction measured at the upper entry with a sharp-edged geometry was related to the liquid flow rate. The critical wavelength based on the theory of interfacial wave instability presented by Imura et al. was only correlated with the tube diameter for the upper entry with a sharp-edged geometry. The correlation and the void fraction relationship to the liquid flow rate at the upper entry produced good predictions of flow rates at the onset of flooding.
Instability of numerical flow analysis at high Reynolds number is caused by spurious high-wave-number oscillations which are produced by the convection term of the Navier-Stokes equation. To correct the instability, some finite difference methods for the convection term have been proposed, such as the QUICK method, the QUICKEST method and the third-order upwind difference method. In this paper, the stability and accuracy of typical finite difference methods, i.e., the 2nd-order centered difference method, the QUICK method, the 3rd-order upwind difference method, the QUICKEST method, the 4th-order centered difference method, the 5th-order upwind difference method and the 6th-order centered difference method, are evaluated by computing the three-dimensional advection equation, i.e., the rotating sphere problem. The 3rd-order Adams-Bashforth method is mainly applied as a time integration method.
In the present paper, direct numerical methods by which to simulate the spatially developing free shear flows in the transitional region are described and the numerical results of a spatially developing plane wake are presented. The incompressible time-dependent Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes of the Orr-Sommerfeld equations were used to perturb the inlet of the wake. Statistical analyses were performed and some numerical results were compared with experimental measurements. When only the fundamental mode is forced, the energy spectra show amplification of the fundamental and its higher harmonics. In this case, unperturbed alternate vortices develop in the saturation region of the wake. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the fundamental structure are observed. Pairing of vortices of the same sign is observed, as well as vortex coupling of vortices of the opposite sign.
The turbulence-generating mechanism in the intake and compression processes of an engine with a square cylinder is investigated by performing a three-dimensional numerical simulation. Emphasis is placed on the influences of the intake turbulence and the compression effect on the TDC (Top Dead Center) turbulence. The compressible Navier-Stokes equations are solved without any explicit turbulence models. The employed numerical algorithm is an extended version of the ICE method, and the third-order upwind scheme is employed for the convective terms. The obtained computational results agree well with the experimental visualization using freon as the working fluid under the condition with a Mach number in excess of 0.5. It is shown that the drastic transition to turbulence near TDC is grasped by computations using this numerical method.
A numerical scheme analyzing unsteady two-dimensional incompressible viscous flow using a general curvilinear coordinate grid is proposed. In this scheme, the unsteady Navier-Stokes equations are solved by a convective-difference scheme using a staggered square grid in transformed space and an interpolation formula considering TVD concept, and an elliptic equation of pressure is solved by the iteration scheme. The continuity condition in the scheme is identically satisfied, and the spurious errors are completely removed, in a manner similar to the MAC scheme. As numerical examples the square cavity, U-type duct and backward-facing step duct flows were calculated. The calculated results show that the scheme has a good accuracy as a second-order scheme and is stable for high Reynolds numbers flow.
An investigation was conducted into the generation of a disturbance wave on a liquid film flowing down a heated inclined plane. Theoretical analysis based on the instability caused by both dynamic and kinematic waves shows that the Marangoni effect due to the surface tension gradient contributes to reduction of the critical flow rate of the liquid on the occurrence of a disturbance wave. Theoretical results also suggest the existence of two boundaries on generation of a disturbance wave at a fixed inclined angle. The flow pattern of a liquid film flowing down a heated brass duct was examined. It was found that one of the boundaries which corresponds to the existence of the disturbance wave is qualitatively consistent with the theoretical result ; the lower boundary, however, could not be observed because liquid film breakdown occurred before the lower critical flow rate was achieved. The measured velocity of a disturbance wave and the wave height are also discussed in comparison with previous results from isothermal liquid film flow.
Spanwise eddy diffusivity of heat was measured in a flat-plate turbulent boundary layer with a constant spanwise temperature gradient and different intensities of free-stream turbulence. Comparison was made with the usual kinematic eddy viscosity measured in parallel. According to the experimental results, the ratio of these eddy diffusivities is strongly influenced by the free-stream turbulence. However, in the vicinity of the wall, this ratio approaches a certain universal distribution which is independent of the intensity of free-stream turbulence.
In this report, to discuss natural-convection film-boiling heat transfer around horizontal cylinders in the small-diameter region, analytical solutions are derived for subcooled film boiling with a smooth liquid-vapor interface. Next, film boiling experiments around thin horizontal wires are conducted for water and R113 at atmospheric pressure. Results of the experiments indicate that, compared with analyses assuming a smooth interface, saturated film-boiling heat transfer in the small-diameter region is enhanced by both rosary-vapor-film and thick-vapor-film effects. As for the effect of liquid subcooling on film-boiling heat transfer in the small-diameter region, it is found that the small-diameter region can be subdivided into normal and singular regions. In the singular region, heat-transfer coefficients decrease to a minimum with increasing liquid subcooling.
An analytical study has been performed on the spray cooling of a hot surface in the region associated with film boiling under the assumption that there will be two parallel conductances of heat transfer. One is of radiation from the hot surface to the environment, the correlation of which is cited from the authors' preceding report(1). The other is heat transfer to the sprayed water droplets by heat conduction through the hypothetical uniform vapor layer underneath the droplet which is in the spheroidal state with a flat bottom. First, we deduce analytically an expression for heat transfer per droplet by solving the equations of momentum in the vapor layer, energy balance at the interface and balance of static forces exerting on a droplet simultaneously. Then a semiempirical correlation of the mean lifetime of the droplets is estimated using the experimental data with surface superheating below 500K at atmospheric environmental pressure, mass velocity of water between 0.0162 and 0.174kg/(m2·s), volume mean diameter of droplets between 130 and 550μm and Weber number between 10 and 120(1). The procedure we propose predicts the heat transfer data of spray cooling within the experimental range mentioned above fairly well.
A procedure using the generalized least squares method was applied to a simple convective heat transfer problem. The potential of the procedure as a tool to facilitate an interactive computational-experimental methodologies (ICEME) was presented. Possibilities were pointed out to reduce experimental inaccuracy and to find the most probable value and its uncertainty of calculated results. Some numerical results of convective heat transfer for a fully developed state of laminar flow in a circular tube have been presented and the usefulness of the studied approach is demonstrated for problems with uncertainties.
Instantaneous heat flux flowing into wall surfaces of combustion chambers used to be analyzed by the use of waveforms of instantaneous temperatures measured by thin-film thermocouples. Such analyses, however, were in fact conducted using known fixed values of the thermophysical properties. In this study, the instantaneous heat flux has been studied by means of numerical analysis using differential equations (to which was added a heat storage term) taking into account the temperature dependency of the thermophysical properties. In addition, related measured values in the previous paper have also been studied again. As a result, it has been concluded that the temperature dependency of the thermophysical properties should be considered when analyzing instantaneous heat flux.
An experimental study was conducted to determine the time histories of fuel vapor concentration and its fluctuation in the combustion chamber of a spark ignition engine. Laser Rayleigh scattering was applied for remote, nonintrusive, point probing of the vapor concentration in the combustion chamber, which was caused by the continuous injection of Freon-12 into an intake port. The conventional engine was modified to make the optical diagnostics accessible. The results showed that the concentration fluctuation consisted of a temporal concentration fluctuation in a specific cycle and a cyclic variation of the temporal mean concentration in this particular cycle, which could be separated and measured accurately by the present experimental apparatus. It was also found that the concentration fluctuation increased and reached a maximum, after which it decreased during the intake and compression strokes. The concentration fluctuation was largely affected by the air fuel ratio and the engine speed.
The effect of heat release on flow-combustion interaction is investigated by the numerical simulation of a non-premixed, temporally developing reacting mixing layer. The chemical reaction considered is a binary, one-step, irreversible model. The results are obtained at different heat release parameters, showing, in qualitative agreement with the existing studies, that the growth of instabilities in the mixing layer is suppressed by heat release, and due to the overall effect of baroclinic and volumetric expansion, the well-created large-scale structures existing in the cases under low or no heat release are weakened and destroyed ; i.e., the rate of chemical product formation and the strength of vorticity decrease with the increasing rate of heat release.
A simulation model developed for research and development of the Stirling engine known as NS 30 S is discussed in this paper. This model is based on the 3rd-order method, for which fundamental equations are derived from the conservative equations of mass, momentum and energy, and numerical model of the system for balancing pressures in four cylinders is included to correspond with the double-acting type Stirling engine NS 30 S. The calculated results are inspected in comparison with the experimental results. Also, by means of the developed simulation model, a comparative study of the engine performance in the case employing helium and hydrogen as the working gas is conducted from the viewpoint of thermophysical properties, and, by clarifying the characteristics of heat transfer and gas flow, the effects of the temperature conditions for driving are investigated. In addition, the particulars of the heat exchangers are evaluated as to design optimization.
Heat transfer characteristics in heated tubes under periodically reversing flow conditions have been experimentally investigated, using a test apparatus that simulates heat exchangers for an actual Stirling engine. It is shown that the heat transfer characteristics under these conditions are greatly affected by the piston phase difference that generates the reversing flow of working fluid, and this phenomenon is peculiar to heat transfer under periodically reversing flow, which is different from the conventional convective heat transfer under steady flow. The experimental correlation for the heat transfer coefficient under these conditions is induced through the use of the working gas velocity evaluated from the Schmidt cycle model, which is one of the ideal Stirling cycles concerning the influence of the piston phase difference.
The heat transfer performance of the actual heat exchangers obtained from the experimental results of the test Stirling engine is presented. The heater for the test engine has 120 heat transfer tubes that consist of a bare-tube part and a fin-tube part. These tubes are located around the combustion chamber and heated by the combustion gas. The cooler is the shell-and-tube-type heat exchanger and is chilled by water. It is shown that the experimental results of heat transfer performance of the heater and cooler of the test Stirling engine are in good agreement with the results calculated by the correlation proposed in our previous heat transfer study under the periodically reversing flow condition. Our correlation is thus confirmed to be applicable to the evaluation of the heat transfer coefficient and the thermal design of the heat exchangers in the Stirling engine.
Numerical analysis using the computer is useful in predicting and evaluating the performance of the Vuilleumier (VM) cycle machine in research and development. The 3rd-order method must be employed particularly in the case of detailed analysis of performance and design optimization. This paper describes our simulation model for the VM machine, which is based on that method. The working space is divided into thirty-eight control volumes for the VM heat pump test machine, and the fundamental equations are derived rigorously by applying the conservative equations of mass, momentum, and energy to each control volume, using staggered mesh. These equations are solved simultaneously by the Adams-Moulton method. Then, the test machine is investigated in terms of the pressure and temperature fluctuations of the working gas, the energy flow, and the performance at each speed of revolution. The calculated results are examined in comparison with the experimental ones.
This paper presents the results of thermodynamic cycle analysis of the single-stage compression heat pump with solution circuit (CHPSC) and the absorption heat pump with booster compressor (AHPBC) with the new working pairs, i.e., R21-NMP, R22-NMP, R21-DMA and R22-DMA. The cycle analysis of a compression heat pump with R22 as the working fluid in also given for comparison. The analysis considers irrever-sibilities due to effectiveness and efficiency of components in the circuit. The coefficients of performance (COP) are fitted as functions of the low-grade source temperature, the temperature at which useful heat is obtained, and ambient temperature. R21-DMA in the AHPBC mode and R21-DMA and R21-NMP in the CHPSC mode yield the best performance. CHPSCs are suitable as peak thermal load units. AHPBCs are useful where temperatures higher than those provided by simple absorption or absorption-resorption heat pumps are desired.