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This study presents an approach to study the three-dimensional internal leakage gas flow occurring in a lubricant-free revolving vane compressor. In this study, the two-dimensional analytical analysis was first carried out using Fanno flow through the leakage paths. This is then expanded by computing the equivalent width of the leakage path which was obtained from a comprehensive three-dimensional computational fluid dynamics model, to form a three-dimensional analytical leakage flow model. Thereafter, measured data from the physical prototype was collected and used to formulate a set of effective leakage flow coefficients. The resultant three-dimensional leakage model was then used to predict the internal leakage flow in the lubricant-free compressor. The results show that the proposed three-dimensional internal leakage model was able to predict the internal leakage of the compressor within discrepancies of ±15%. Subsequent studies show that with better machining tolerance control, a practical volumetric efficiency above 90% can be achieved by the lubricant-free revolving vane compressor. Nanyang Technological University The authors would like to acknowledge Nanyang Technological University for funding.

In this chapter, we look at one-dimensional adiabatic flow in a duct with friction at the walls of the duct. This type of flow occurs, for example, when gases are transported through pipes over long distances. It is also of practical importance when equipment handling gases are connected to high-pressure reservoirs, which may be located some distance away. Knowledge of this flow will allow us to determine the mass flow rate that can be handled, pressure drop and so on.

A novel rotating piston-type compressor is presented. The conventional rolling piston architecture was redesigned to allow oil-free operation. The spring activated vane was replaced by a directly driven swinging vane to provide constant contact to the rotating piston. The model of the compressor was implemented in the AMESim simulation platform. Experiments were conducted on prototypes and the data were evaluated based on the simulation results. Directly unobservable geometric dimensions were estimated by adjusting the mathematical model parameters to the measured thermodynamic state variables with the use of a multi-parametric genetic algorithm. The simple genetic algorithm proved fast and adequate solutions. According to the collected results, the oil-free rotating piston architecture is significantly more sensitive to the sealing clearances compared to the conventional oil lubricated rolling piston compressors. Therefore, the theoretically estimated performance can only be achieved with extremely small manufacturing tolerances, which has to be maintained during the operation.

Theoretical and numerical studies have been carried out for establishing the novel concept of the boundary-layer induced Sanal-flow-choking in high velocity transient (HVT) solid propellant rocket motors with sudden expansion / divergent port. The Sanal-flow-choking for the diabatic flow is a unique condition of any real-fluid-flow problem at which both the thermal-choking (Rayleigh flow effect) and the wall-friction induced flow-choking (Fanno flow effect) occur in a single fluid-throat region. We proved conclusively that at the subsonic igniter jet flow condition any dual-thrust motor (DTM) with large upstream port-length-to-diameter (l/d) ratio predisposes to the deflagration-to-detonation-transition (DDT) creating pressure-overshoots leading to the catastrophic failure of the HVT DTM as a result of the Sanal-flow-choking phenomenon and generation of strong shock waves. The detonation kernel is more susceptible in HVT DTMs producing the dominant reacting species with low heat capacity ratio. We observed that the flame spread acceleration is relatively higher for the DTM cases with the high propellant loading density, within the given envelop with large l/d ratio, owing to the enhanced propellant surface heating due to the boundary-layer heat transfer effects. We concluded that the undesirable detonation in any dual-thrust combustor could be eliminated by maintaining the lower-critical-detonation-index (LCDI) always higher than the total-to-static pressure-ratio at the fluid-throat and/or at the transition region of the combustor. This could be achieved in the HVT DTMs, without reducing the propellant loading density, by breaking the boundary-layer-blockage and/or increasing the heat-capacity-ratio of the gases generating from the igniter and/or the upstream-port of the motor for prohibiting the Sanal-flow-choking condition. We concluded that the l/d ratio, the heat capacity ratio of the species, total-to-static pressure ratio at the fluid-throat and the rheology of the fluid linking together determines the boundary-layer induced internal flow choking and detonation in DTMs. The concept of a critical detonation kernel established herein throws light to the global scientific community on the fundamental mechanism of the DDT in dual-thrust rockets.

This paper presents an experimental study of airflow from convergent-divergent nozzles discharged into enlarged duct, focusing attention on the flow development in the duct. To investigate the influence of active control on the flow field developed in the duct, the micro jets of 0.05 mm radius orifice placed at 900 interval along the base at 6.5 mm from the main jet were employed. The Mach number of this study was 1.3. The area ratio of the present study was 2.56. The NPR presented are from 3, 5, 7, 9, and 11 respectively. The L/D ratio of the duct was varied from 10 to 1. The level of expansion at the nozzle exit influences the wall pressure very strongly since in the present case all the NPRs of the tests are under expanded. For all the L/D the entire flow field in the duct is full of waves, the few shock wave is so powerful that the wall pressure is equal to the atmospheric pressure or more. At L/D = 3, it is seen that due to the influence of the back pressure the number of compression and expansion waves have reduced drastically. The flow field with and without control is identical.

A numerical model of the internal flow in a duct rotating about one end is described. One-dimensional Euler equations are solved inside the duct using a finite volume formulation in which the advective fluxes are calculated using the advection upwind splitting method. The model was developed as a fast design tool for helicopter rotor blades with internal spanwise flow. To this end, centrifugal as well as Coriolis effects, frictional losses, duct sweep, and time-dependent duct boundary conditions are modeled, and a spanwise flow control valve can be included. The model is used to explore the behavior of a 2-m-long duct with a circular cross section, rotating at tip speeds of up to 260 m/s. The effects of centrifugal pumping, duct friction, duct sweep, and a flow control valve on the spanwise pressure and velocity distribution, mass flow rate of air through the duct, and torque required to spin the duct are discussed.

Local friction factors of laminar and turbulent gas flows including choked flows through micro-tubes were experimentally investigated under atmospheric back pressure and variable inlet pressure. The experiments were carried out using two glass micro-tubes with D = 265.7 and 399.9 μm and a fused silica micro-tube with D = 531.2 μm. Two to three pressure tap holes were drilled into the micro-tube wall at intervals of 5 ~ 6 mm to measure local pressures. The local Mach numbers, temperatures and friction factors were obtained by using stagnation temperatures and pressures, local pressures and mass flow rates. The results for wide range of Reynolds numbers and Mach numbers were obtained including choked flows. Both the local Fanning and the local Darcy friction factors were obtained under the assumption of both Fanno flow (adiabatic wall) and isothermal flow, respectively. Since the measured values of the inner relative surface roughness of the micro-tubes were less than 0.02 %, only the effect of compressibility on friction factors was assessed. The difference between Fanning and Darcy friction factors was described and compared with the ff and fd correlation as a function of Mach number. The friction factor difference obtained under the assumption of Fanno and isothermal flows was also compared with the available literature and numerical results. In the turbulent flow region including the choked flow, the local Fanning friction factors under the assumption of Fanno flow nearly coincided with Blasius correlation.

International audience; This paper presents data reduction of average friction factor of gas flow through adiabatic micro-channels. In the case of micro-channel gas flow at high speed, the large expansion occurs near the outlet and the pressure gradient along the length is not constant with a significant increase near the outlet. This results in flow acceleration and a decease in gas temperature. Therefore the friction factor of micro-channel gas flow should be obtained with measuring both the pressure and temperature. The data reductions on friction factors were carried out under the assumption of isothermal flow for numerous experimental and numerical studies since temperature measurement International Journal of Heat and Mass Transfer 2 of micro-channel gas flow at high speed is quite difficult due to the measurement limitations. In the previous study, it was found that the gas temperature can be determined by the pressure under the assumption of one dimensional flow in an adiabatic channel (Fanno flow). Therefore in the present study data reduction to estimate friction factors between two relatively distant points considering the effect of a decrease in temperature is introduced with the temperature determined by the measured pressure at a specific location. The Friction factors obtained by using the present data reduction are examined with the available literature and the results are compared with empirical correlations on Moody chart.

This paper studies steady motion of gas in a rectilinear duct with square cross-sections,governed by the three-dimensional (3-d) non-isentropic compressible Euler equations with a friction term.Such flows are called Fanno flows in engineering. We construct respectively special subsonic flows, supersonic flows and transonic shocks in the duct.Since the 3-d steady compressible Euler equations are of quasi-linear hyperbolic-elliptic composite type for subsonic flows, and there is no generaltheory up to now, we formulate a boundary value problem arising from studies of transonic shocks, and prove the well-posednessof this problem by showing that the special subsonic flows constructed above are stable under small multi-dimensional perturbations.The proof depends on separation of the elliptic and hyperbolic parts in the Euler equations, and designation of a suitable nonlinear iteration scheme.Particularly, there are strong interactions between the elliptic part and the hyperbolic part due to the appearance of friction, and we deducea linear mixed boundary value problem of a second-order elliptic equation with an integral-type nonlocal term. Its well-posedness is establishedby applying methods of Fourier analysis and regularity theory of second-order elliptic equations.

Miniature flow passages, defined here as passages with hydraulic diameters smaller than about 1 mm, have numerous applications. Some current applications include monolith chemical reactors, inkjet print-heads, bioengineering and biochemistry (lab-on-the-chip; drug delivery with ultrathin needles, etc.), microflow devices (micropumps, micro heat exchangers, etc.), and cooling systems for microelectronic and high-power magnets, to name a few. Miniature flow passages are an essential part of microfluidic devices , in which can be broadly defined as devices in which minute quantities of fluid are applied. Cooling systems based on microchannels can provide very large volumetric heat disposal rates that are unfeasible with virtually any other cooling technology. Their widespread future applications may in fact revolutionize some branches of medicine and industry. The serious study of flow in capillaries (tubes with D ≈ 1 mm) goes back to at least the 1960s. The application of microchannels for cooling of high-power systems is relatively new, however (Tuckerman and Pease, 1981). The literature dealing with flow in microtubes is extensive. Useful reviews include those of Papautsky et al. (2001), Morini (2004), Krishnamoorthy et al. (2007), and Fan and Luo (2008). The field of flow in miniature channels, in particular with respect to very small channels (microfluidics and nanofluidics) is a rapidly developing one. In this chapter we review the flow regimes and size-based miniature flow passage categories, and we discuss the limitations of the classical convection heat and mass transfer theory with respect to its application to miniature flow passages.

Intermediate turbine duct represent the flow path between the high pressure and low pressure turbine. Caused by the complex flow mechanism, the outlet flow condition of the high pressure turbine is easily changed. Since the upstream flow condition from the high pressure turbine has a significant effect on the internal flow field of intermediate turbine duct, the study in the upstream condition is of high value. Through numerical simulation, the influence of upstream flow angle variation on intermediate turbine duct is observed. It is found that the main influence of the flow angle variation is near the hub side of the duct, and the quantitative result shows that a larger flow angle has a positive effect on the flow field and can reduce loss.

In this research, experiments are performed to study the laminar flow mixed-convection heat transfer with radiation effects for a hydrodynamically fully developed and thermally developing airflow in a horizontal duct. The duct cross section is made of two differentially heated isothermal vertical walls and two adiabatic horizontal walls with aspect ratios 1 and 0.5. The total heat transfer from the hot wall to the cold wall of the duct depends on the mixed convection and also on the surface radiation heat transfer that takes place within the duct. The analysis of experimental data for the Nusselt number from the hot wall of the duct shows that it is important to consider the effects of surface radiation, and to accounted for them, in the design and analysis of flow and heat transfer through ducts. The flow field within the duct is also made visible by a suitable smoke flow visualization method. The heated air moves upward, accumulates near the top wall adjacent to the hot wall of the duct, and gets circul...

Ejector refrigeration systems are less power intensive when compared to conventional refrigeration cycles, mainly due to their ability to use low-grade heat sources to reduce electrical power requirements. The efficiency of these systems is largely dominated by the performance of the ejector. Therefore, it is essential that the performance characteristics of the ejector are predicted using a mathematical model to aid design analysis. Though numerous mathematical models of ejectors exist, this paper improves upon the one-dimensional mathematical model of the ejector and validates its accuracy by comparing it with experimental data available in the literature for the R141b refrigerant. The novelty of this improved model is that Fanno flow concept has been applied to capture frictional compressible flow that is occurring in the mixing chamber of the ejector. In addition, rather than assuming a constant heat capacity ratio γ, the proposed model further enhances the accuracy of the model by averaging the γ between each segment of the flow within the ejector. Validations have revealed that the entrainment ratio was predicted within 4% absolute error, while the condenser operating pressure predictions have an average absolute error of 5% with respect to experimental measurements.

Numerical simulations of fully-developed turbulent flow through a straight square duct at three Reynolds numbers of 190, 300, and 550 based on the friction velocity averaged over the duct perimeter and duct half width are reported. The effect of Reynolds number on the mean and turbulence statistics and secondary flow is investigated. The mean streamwise-velocity profiles along the wall bisector are found to obey a logarithmic scaling when they are normalized by the friction velocity at the mid-wall. Magnitudes and spatial distributions of the peak production and diffusion terms in the mean streamwise-vorticity equation normalized by the wall units are found to be unaffected by the Reynolds-number variation when they are considered in wall-unit coordinates.

The method of energy separation in a high-speed flow proposed by A.I. Leontyev is investigated numerically. The adiabatic compressible gas flow (of a helium-xenon mixture) with a low Prandtl number in a planar narrow duct and a flow with heat exchange in a duct partitioned by a heat-conducting wall are analysed. The temperature recovery factor on the adiabatic wall, degree of cooling the low-speed flow part, temperature efficiency, and the adiabatic efficiency in a duct with heat exchange are estimated. The data are obtained for the first time, which make it possible to compare the efficiency of energy separation in a high-speed flow with the efficiency of similar processes in vortex tubes and other setups of gas-dynamic energy separation.

Experimental studies of turbulent flow through a triangular duct with small apex angle of 11.5° performed by Eckert and Irvine (1956) show flow laminarisation in the corner region of the duct. This effect is re-investigated using direct numerical simulation (DNS). In order to analyze the impact of duct corners on the flow behavior, results for the friction factor and the mean velocity profiles arising from different non-circular duct geometries, namely a square duct, an equilateral triangular duct and isosceles triangular ducts with an apex angle of 11.5° and 4° are compared with the results for circular pipe flow. Within the cross-sections of the ducts with the small apex angles, regions of essentially laminar and turbulent properties are found to exist simultaneously. From analysis of the turbulent quantities performed exemplary for the 11.5°-triangle we gain further insights into the mechanisms responsible for flow laminarization which are supported by analytical considerations for statistically axisymmetric turbulence.

The aim of this note is to obtain a flow rate equation for subsonic Fanno flow, which has a form similar to the flow rate equation for isothermal flow. When pipe dimensions and the proper values of pressures and temperatures at two sections along a pipe, namely P1, P2, T1 and T2 are given, the mass flow rate is obtained by simple substitution into the obtained formula. However, only three of the above four quantities are independently given, since the steady Fanno flow problem involves three first-order differential equations. Therefore, the problem has three degrees of freedom. The theory in this note shows an algebraic equation that determines the fourth quantity by using the given three quantities. The method for finding the mass flow rate and state variables of the gas in the pipe are substantially simplified compared with the commonly distributed method. The relative difference of mass flow rates between the subsonic Fanno and isothermal flows is smaller than 1% in practical combinations of P2 /P1 and the pipe-friction parameter fL/D.

Full-bore decompression of an initially highly pressurized pipe has been studied extensively in recent years. The main aim of this effort has been to estimate the speed of the decompression wave and its relationship to the speed of a travelling fracture in the pipe wall. It has been demonstrated that the speed of the decompression wave is influenced by the friction at the gas-solid interface, and also by the pipe size (diameter). The numerical value of the friction factor has been traditionally estimated using known relationships such as the Haaland formula. However, it has also been noticed that the friction factor calculated in this way has to be increased many-fold to achieve agreement between theory and experiment. To date, there is no physical justification for this increase. The present paper proposes an explanation by modelling the full-bore decompression as a ‘transient Fanno’ flow. The model development is based on the observation that the flow at the exit plane always tends to approach a ‘choked’ condition (sonic velocity). It is shown that a re-interpretation of the Fanno flow formula allows an estimation of the irreversibility, and therefore the friction factor, in the evolving flow. When averaged over space and time, the friction factor attains a value that need not be artificially adjusted. This value of the friction factor can be used in one-dimensional models of the decompression process. Also, the role of the ‘second coefficient of viscosity’ during the initial instants of the highly transient flow is examined.

A recent paper of Ockendon et al. discusses the Fanno model for quasi-one-dimensional flow of gas in a tube, in situations where the flow is turbulent and the tube is long enough for wall drag to be important. Based on appropriate scalings and with associated boundary conditions they derive equations for similarity solutions and make predictions about travelling and evolving waves. In this paper the existence, uniqueness and asymptotic behaviour of these wave forms is proved rigorously. Techniques include shooting methods (both one- and two-parameter), appropriate changes of variables, and comparison techniques.

The phenomenon of choked flow has been recognized and understood for many decades. These flows also have a variety of practical applications, such as pneumatic systems, oil and gas well blowouts, and vents in high-pressure systems, among others. According to some recent experiment data carried out in a straight pipe, the flow Mach number exceeds unity at the exit of pipe. This conflicts the Fanno flow theory that has long been applied to the one-dimensional gas dynamics area. At present, it is not clear whether this comes from experimental errors or any other reasoning that was not yet disclosed. There may be a suspected possibility of boundary layer thinning near the duct exit, which accounts for a divergent flow passage. The main objective of the present effort is to understand the flow mechanism by which the main flow Mach number exceeds unity near the exit of a straight duct. Both computational and theoretical analyses have been performed to investigate the detailed choking phenomenon at the vicinity of duct exit. The results obtained show that boundary layer thinning is produced by the flow at the vicinity of duct exit, with subsonic inlet conditions, consequently leading to the divergent flow passage. The sonic conductance is analysed in terms of pressure loss and boundary layer blockage with different duct sizes.

This paper investigates the inertial and creeping flow of a second-order fluid in a curved duct with a square cross-section. Numerical modeling is employed to analyze fluid flow, and the governing equations are discretized using the finite difference method on a staggered mesh. The marker-and-cell method is employed to allocate the parameters on the staggered mesh, and static pressure is calculated using the artificial compressibility approach. The effect of centrifugal force due to the curvature of the duct and the opposing effects of the first and second normal stress difference on the flow field are investigated. In addition, the order-of-magnitude technique is used to derive the force balance relations for the core region of flow. Based on these relations, the performance mechanism of centrifugal force and normal stress differences on the generation of secondary flows is considered. We also present an analytical relation for the axial velocity profile and flow resistance ratio of creeping flow. For this kind of flow, previous studies have investigated the effect of the first normal stress difference on the transition from one pair to two pairs of vortices while we show that the negative second normal stress difference has the opposite effect on this transition and can stabilize the flow.

In this paper, we consider the unsteady flow of an incompressible second grade fluid in a circular duct with a given volume flow rate variation. The effects of Hall current are taken into account. The governing equations are solved analytically using Laplace transform method. The velocity profiles are constructed for the four cases: (a) constant accelerated flow (b) sudden started flow (c) the flow rate has a trapezoidal variation with time (d) starting from rest the volume flow rate oscillates sinusoidally. The present analysis is more general than any previous investigation.

Properties of fully developed viscous flow through a super-elliptic duct are reported. The cross section resembles rectangular ducts with rounded corners. The effect of corner rounding depends on the aspect ratio, and in general decreases both flow and convective (H1) heat transfer but increases minimum wall shear stress. An accurate, efficient Ritz method is used.

Three-dimensional simulations of laminar buoyancy assisting mixed convection in a vertical duct with a plane symmetric sudden expansion are presented to illustrate the effects of the buoyancy assisting force and the duct’s aspect ratio on the flow and heat transfer. This geometry and flow conditions appear in many engineering applications, but 3-D heat transfer results have not appeared in the literature. This study focuses on the regime where the flow and thermal fields are symmetric in this geometry. The buoyancy force is varied by changing the heat flux on the stepped walls that are downstream from the sudden expansion, and the duct’s aspect ratio is varied by changing the width of the duct while keeping the expansion ratio constant. Results are presented for duct’s aspect ratio of 4, 8, 12, 16, and ∞ (2-D flow), and for wall heat fluxes between 5–35 W/m 2 . The Reynolds number and the range of wall heat flux are selected to insure that the flow remains laminar and symmetric in this geometry and reverse flow does not develop at the exit section of the duct. Results for the velocity, temperature, and the Nusselt number distributions are presented, and the effects of the buoyancy force and the duct’s aspect ratio on these results are discussed.

We considered the so-called Fanno flow as a model of flow through pneumatic pipe lines with a constant diameter. The flow is one dimensional, steady and adiabatic. The friction coefficient is constant. We succeeded to express the critical pressure ratio of the flow which is choking at the exit of the pipe line by three parameters, the pipe diameter, the pipe length and the friction coefficient. We compared the theoretically estimated critical pressure ratio to the experimental results. The results showed the good agreements except the case of the short pipe lines less than 10 cm. It was confirmed that our method of determination of the ratio was very useful for the flow calculation using ISO choke equation. With these studies we established the simulation program for the Fanno flow on MATLAB_Simulink and show that the program was easily applied to connected pipelines in series.

Large scale, three dimensional computer simulations of monosized, viscoelastic, spherical glass particles flowing in an inclined duct were performed using a phenomenological model based on the modified Kelvin–Maxwell model. The particle flow rate in the model duct was regulated using a stationary wedge located in the middle of the duct. At low flow rates of glass particles, a continuous flow was observed similar to that excited by steadily and rapidly adding glass particles to the top of a heap. However, at high flow rates, a totally different situation arises where a flow with a different nature was established in the duct. The situation was found to be analogous to the case of a supersonic gas flow in a duct, where a curved-bow shock was observed to have formed on the upper edges of the duct adjacent to the wedge. In addition, in supersonic granular flows the viscous and conductance effects spread the shock changes over a finite shock layer.

In this paper we study the transonic shock in steady compressible flow passing a duct. The flow is a given supersonic one at the entrance of the duct and becomes subsonic across a shock front, which passes through a given point on the wall of the duct. The flow is governed by the three-dimensional steady full Euler system, which is purely hyperbolic ahead of the shock and is of elliptic–hyperbolic composed type behind the shock. The upstream flow is a uniform supersonic one with the addition of a three-dimensional perturbation, while the pressure of the downstream flow at the exit of the duct is assigned apart from a constant difference. The problem of determining the transonic shock and the flow behind the shock is reduced to a free-boundary value problem. In order to solve the free-boundary problem of the elliptic–hyperbolic system one crucial point is to decompose the whole system to a canonical form, in which the elliptic part and the hyperbolic part are separated at the level of the principal part. Due to the complexity of the characteristic varieties for the three-dimensional Euler system the calculus of symbols is employed to complete the decomposition. The new ingredient of our analysis also contains the process of determining the shock front governed by a pair of partial differential equations, which are coupled with the three-dimensional Euler system.

This paper presents numerical results on the evolution of the solutions of the Fanno model for compressible pipe flow. The principal results concern the large-time behaviour when nonlinear effects are appreciable throughout the evolution. Our computations show that compression waves can be expected to evolve into travelling waves for large times whereas expansion waves cannot.

An experimental study was performed on the choking due to the friction in supersonic Fanno flows in long constant-area ducts. The results show that the choking condition of the flow is much different from the calculated value by the previous one-dimensional theory. For a given inlet Mach number and a friction coefficient of a duct, for example, the maximum possible length of the duct is shorter than that predicted by the theory. The reason has been well explained by replacing a normal shock wave assumed in the theory by a pseudo-shock wave in real flow.

The present study investigates the flow and heat/mass transfer characteristics of wavy duct for the primary surface heat exchanger application. Local heat/mass transfer coefficients on the corrugated duct side walls are measured using a naphthalene sublimation technique. The flow visualization technique and a numerical analysis using a commercial code, FLUENT, are used to understand the overall flow structures inside the duct. The corrugation angle of the wavy duct is 145° and the duct aspect ratio is 7.3. The Reynolds numbers, based on the duct hydraulic diameter, vary from 100 to 5000. The results show that complex secondary flows and transfer processes exist inside the wavy duct resulting in non-uniform distributions of the heat/mass transfer coefficients on the duct side walls. At low Reynolds numbers ( Re ⩽ 1000), relatively high heat/mass transfer regions like cell shapes appear on both pressure- and suction-side walls due to the secondary vortex flows called Taylor–Gortler vortices perpendicular to the main flow direction. However, at high Reynolds numbers ( Re > 1000), these secondary flow cells disappear and boundary layer type flow develop on pressure-side wall. On the suction-side wall, high heat/mass transfer region appears by the flow reattachment. The average heat/mass transfer coefficients are higher than those of the smooth circular duct and pressure drop increases due to the secondary flows inside wavy duct.

Results of a numerical study of a laminar separated flow behind a rectangular step on a porous surface with uniform injection or suction are described. Two cases are considered: an unconfined flow past a step and flow evolution in a confined channel (duct). It is shown that mass transfer on the surface causes strong changes in the flow structure and substantially affects the position of the reattachment point, as well as friction and heat transfer. More intense injection leads first to an increase in the separation-zone length and then to its rapid vanishing due to boundary-layer displacement. Vice versa, suction at high Reynolds numbers Res > 100 reduces the separation-zone length. The duct flow has a complicated distribution of friction and heat-transfer coefficients along the porous surface owing to the coupled effect of the transverse flow of the substance and changes in the main flow velocity due to mass transfer.

The three-dimensional flow structure induced by normal shock-wave/turbulent boundary-layer interaction in a constant-area rectangular duct is investigated by a laser-induced-fluorescence method. This diagnostic system uses an argon-ion laser as a light source, and the target gas is dry nitrogen with iodine seeded as a fluorescence material. The Mach-number distributions in the duct are obtained from the measured fluorescence intensity, and the threedimensional flow pattern in the expansion region downstream of the initial shock wave is clarified. In addition to this, the region having locally higher Mach number near the duct corners is observed immediately behind the shock wave, and the three-dimensional shape of the boundary layers is found. These flow characteristics are reproduced by solving the Navier‐Stokes equations numerically. The calculated result reveals that the complicated shock-wave configuration is formed at the duct corner because of the interaction of two bifurcated shock waves developed on the two perpendicularly adjacent walls. The simple flow model is also constructed by considering this interaction. This model can explain very well the three-dimensional flow characteristics.

This article considers the effects of the side walls on the unsteady flow of an incompressible viscous fluid in a duct of uniform cross-section. In order to show the effects of the side walls, three illustrative examples are given. They are: the starting flow in a duct of semicircular cross-section, the starting flow in a duct of rectangular cross-section and the starting flow in a duct of circular cross-section. The velocity distributions and the volume fluxes obtained for these flows are compared and it is shown that the flow in a duct of semicircular cross-section reaches steady state earlier than those for the flow in a duct of circular cross-section and for the flow in a duct of square cross-section. It is found that there are remarkable effects of the side walls of a duct on the required time to attain the asymptotic values of flow properties.

The unsteady flow of an incompressible Oldroyd-B fluid in a circular duct embedded in a porous medium is studied. The fluid is conducting in the presence of a transverse magnetic field and the influence of Hall currents is investigated. The motion in the duct is generated by a given but arbitrary time dependent inlet volume flow rate. Laplace transform technique is used to determine the exact solutions for the four cases: (a) constantly accelerated flow, (b) sudden started flow, (c) the flow rate has a trapezoidal variation with time and (d) oscillatory flow.

In the present study, the velocity profile and pressure gradient of the unsteady state unidirectional flow of a Voigt fluid in a circular duct with different prescribed volume flow rate are investigated. The flow motion in the duct is induced by a prescribed inlet volume flow rate which varies with time. Based on the flow conditions prescribed, two basic flow situations are solved; these are a suddenly started, and a constant accelerated, flow respectively. These two results are then applied to a practical case that is a trapezoidal motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then maintaining at this velocity, following with the constant deceleration to a stop. In addition, oscillatory flow is also considered.

The Taylor–Dean flow through a curved duct of square cross section, in which walls of the duct except the outer wall rotate around the center of curvature and an azimuthal pressure gradient is imposed, is investigated numerically using the spectral method. The calculation covers a wide range of pressure gradient and duct rotational speed. The steady flow patterns of the induced secondary flow and flux through the duct are obtained. It is found that the secondary flow consists of two vortices in a cross section when the rotation of the duct is large and opposite to the negative pressure gradient. When the rotation is in the same direction as the negative pressure gradient, the secondary flow shows more complicated behavior. There appear four-vortex, eight-vortex or even non-symmetric secondary flow patterns with respect to the center line of the cross section. An analysis of linear stability is also carried out.

This paper presents a homogeneous simulation model for choked flow conditions for pure refrigerants (R134a, R600a) in adiabatic capillary tubes. The model is based on the first principles of thermodynamics and fluid mechanics and some empirical relations. This study presents a fresh-look at the classical fluid flow problem, known as ‘Fanno flow’ for refrigerant flow in capillary tubes. A new diagram called the full range simulation diagram has been developed that presents a better way to understand the choked flow phenomenon graphically. The diagram is useful for design and analysis of refrigerant flow in capillary tubes. The model has been validated with published experimental data for R22, R134a and R600a and is found to agree to within ±7%.

The effects of the curvature of the side walls on the flow of an incompressible viscous fluid in a duct of uniform cross-section due to the motion of the top wall and an imposed pressure gradient along the duct are considered. In order to show the effect of the wall curvature, two illustrative examples are given. One of them is the flow in a duct of semicircular cross-section and the other is the flow in a duct of rectangular cross-section. The results obtained for the flow in a duct of semicircular cross-section for zero flux and for separation at the bottom wall are compared with those of the flow in a duct of rectangular cross-section. It is a remarkable effect of the wall curvature on the flow in a duct that the separation at the bottom wall for the flow in a rectangular duct starts earlier than that in a semicircular duct.

In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of an Oldroyd-B fluid in a circular duct are considered. The flow motion in the duct is induced by a given but arbitrary inlet volume flow rate which varies with time. Based on the flow conditions described, two basic flow situations are solved, which are a suddenly started, and a constant acceleration, flow respectively. These two results are applied to a practical case that is a trapezoidal piston motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then keeping at this velocity, following with the constant deceleration to a stop. In addition, oscillatory flow is also considered.

Micro- and conventional compressible, turbulent tube flows were solved numerically in this study. The numerical procedure solves the compressible, turbulent boundary-layer equations using an implicit finite-difference scheme. The parabolic character of the boundary-layer equations renders the numerical procedure a very efficient, accurate, and robust tool for studying compressible microtube flows. The Baldwin–Lomax two-layer turbulence model is adopted in the numerical procedure. The numerically calculated friction factors are compared with the Blasius correlation, the Fanno line flow prediction, and the experimental data. The comparison shows that the numerically calculated friction factors for conventional tube flows agree quite well with the Blasius correlation. The numerical friction factors for microtube flows are larger than the Blasius correlation due to the compressibility effects. They also are greater than the Fanno line flow prediction and the experimental data. This is because the Fanno line f...

The hydrodynamic stability of flow of an incompressible fluid through a plane-parallel channel or circular duct filled with a saturated porous medium, modeled by the Brinkman equation, is discussed on the basis of an analogy with a magneto-hydrodynamic problem (Hartmann flow). Flow in a circular duct is found to be stable to small disturbances for all values of the Reynolds number, but for a plane-parallel channel the flow is unstable if the Reynolds number exceeds a critical value, dependent on a Darcy number.

Experimental flow visualization is conducted here to investigate the buoyancy-induced return flow structure in mixed convection of gas over a heated circular plate mounted on the bottom of a horizontal flat duct, simulating that in a horizontal longitudinal flow reactor. In particular, how the return flow induced in the upstream portion of the duct is related to the vortex flow in the downstream is delineated. The results show that at a low buoyancy-to-inertia ratio only steady longitudinal vortex rolls (L-rolls) are induced in the exit half of the duct and no return flow appears in the duct. At an intermediate buoyancy-to-inertia ratio a small flow recirculation exists around the duct inlet near the top wall and the L-rolls become unsteady. When the buoyancy-to-inertia ratio is high and the Reynolds number is small with Re

This paper is a proposal to design flow structures with maximal heat transfer rate per unit volume, by shaping each duct so that it fits optimally on the body of the convective flow. Optimally shaped ducts can be assembled into larger constructs. Two examples are given. In the first, a heat-generating strip is cooled inside a duct of rectangular cross-section. The duct geometry has two degrees of freedom, which can be selected so that the fixed duct volume packs a maximum of heat transfer rate. In the second example, the duct is a tube with isothermal internal surface, and the flow is sufficiently slow so that boundary layers do not form inside the duct. Once again, the duct aspect ratio can be optimized for maximal heat transfer rate density. Further improvements can be sought by endowing the duct geometry with more degrees of freedom.

The present paper describes a one-dimensional model for a compressible internal flow with mass and heat additions in a constant area duct taking account of the upstream boundary layer. The conservation equations across a control volume are treated one-dimensionally by assuming an appropriate mean flow. This model can estimate the maximum amount of the mass flow rate on the flow choking for a given upstream free Mach number and boundary layer thickness. As the result, a parallel injection can add more amount of mass flow rate than normal injection in the present analytical condition. The characteristics of the flow such as the down stream Mach number, static pressure and total pressure distributions are analyzed with the boundary layer thickness for given upstream condition. Also, the analytical result of the present model shows better agreement with the previous experimental data on the mass and heat additional flows in constant area duct.