Free-Molecule Tube Flow and Adiabatic Wall Temperatures

1963 ◽  
Vol 85 (2) ◽  
pp. 111-118 ◽  
Author(s):  
E. M. Sparrow ◽  
V. K. Jonsson ◽  
T. S. Lundgren
Keyword(s):  
Mass Flow ◽  
Wall Temperature ◽  
Energy Transport ◽  
Circular Tube ◽  
Tube Length ◽  
Tube Flow ◽  
Free Molecule ◽  
Adiabatic Wall ◽  
Flow Through ◽  
Molecule Flow

The processes of mass and convective-energy transport in free-molecule flow are shown to bear useful similarities with the process of energy transport by thermal radiation. These similarities have been applied as a basis for deriving the mass and energy transfer characteristics for free-molecule flow in a circular tube. The net mass flow through tubes of various length-diameter ratios has been calculated as a function of the pressures and temperatures at the inlet and exit of the tube. A throughflow may occur even if the inlet and exit pressures are the same, provided that a temperature difference exists. For a length-diameter ratio in excess of 45, a fully developed mass flow relation applies. The distribution of the adiabatic wall temperature along the tube length has also been determined as a function of system pressures and temperatures and of the tube dimensions. Rather large variations of adiabatic wall temperature may occur for long tubes. The throughflow of energy shows characteristics similar to the throughflow of mass.

Heat Transfer and Forces for Free-Molecule Flow on a Concave Cylindrical Surface

1964 ◽  
Vol 86 (1) ◽  
pp. 1-9 ◽  
Author(s):  
E. M. Sparrow ◽  
V. K. Jonsson ◽  
T. S. Lundgren ◽  
T. S. Chen
Keyword(s):  
Heat Transfer ◽  
Wall Temperature ◽  
Cylindrical Surface ◽  
High Speed ◽  
Angle Of Attack ◽  
Accommodation Coefficient ◽  
Free Molecule ◽  
Adiabatic Wall ◽  
The Difference ◽  
Molecule Flow

An analysis has been carried out to determine the local and overall heat-transfer rates, the adiabatic wall temperature, and the forces exerted when a high-speed, free-molecule flow is incident on a concave cylindrical surface. The flow may impinge on the surface at an arbitrary angle of attack. Additionally, the thermal accommodation coefficient may be arbitrary, and the degree of concavity of the surface may be varied at will from a semicircular cross section to a relatively flat circular arc. The concavity causes molecules to interreflect back and forth between surface elements. Even with the interreflections, the heat-transfer rate continues to depend linearly on the difference between the wall temperature and the adiabatic wall temperature. The interreflections are found to have a greater effect on both the heat transfer and the force results as the accommodation co-efficient decreases and as the degree of concavity and the angle of attack increase.

High Resolution Heat Transfer Measurements on the Stator Endwall of an Axial Turbine

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Benoit Laveau ◽  
Reza S. Abhari ◽  
Michael E. Crawford ◽  
Ewald Lutum
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
High Resolution ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
Mass Flow ◽  
Wall Temperature ◽  
Adiabatic Wall ◽  
Axial Turbine ◽  
The Heat Transfer Coefficient

In order to continue increasing the efficiency of gas turbines, an important effort is made on the thermal management of the turbine stage. In particular, understanding and accurately estimating the thermal loads in a vane passage is of primary interest to engine designers looking to optimize the cooling requirements and ensure the integrity of the components. This paper focuses on the measurement of endwall heat transfer in a vane passage with a three-dimensional (3D) airfoil shape and cylindrical endwalls. It also presents a comparison with predictions performed using an in-house developed Reynolds-Averaged Navier–Stokes (RANS) solver featuring a specific treatment of the numerical smoothing using a flow adaptive scheme. The measurements have been performed in a steady state axial turbine facility on a novel platform developed for heat transfer measurements and integrated to the nozzle guide vane (NGV) row of the turbine. A quasi-isothermal boundary condition is used to obtain both the heat transfer coefficient and the adiabatic wall temperature within a single measurement day. The surface temperature is measured using infrared thermography through small view ports. The infrared camera is mounted on a robot arm with six degrees of freedom to provide high resolution surface temperature and a full coverage of the vane passage. The paper presents results from experiments with two different flow conditions obtained by varying the mass flow through the turbine: measurements at the design point (ReCax=7.2×105) and at a reduced mass flow rate (ReCax=5.2×105). The heat transfer quantities, namely the heat transfer coefficient and the adiabatic wall temperature, are derived from measurements at 14 different isothermal temperatures. The experimental data are supplemented with numerical predictions that are deduced from a set of adiabatic and diabatic simulations. In addition, the predicted flow field in the passage is used to highlight the link between the heat transfer patterns measured and the vortical structures present in the passage.

Free Molecule Flow Through a Vacuum Seal

1970 ◽  
Vol 92 (3) ◽  
pp. 405-410
Author(s):  
H. S. Yu ◽  
E. M. Sparrow
Keyword(s):  
Mass Flow ◽  
Numerical Solutions ◽  
Rarefied Gas ◽  
Coupled System ◽  
Mass Fluxes ◽  
Wide Range ◽  
Flow Through ◽  
Molecule Flow ◽  
Range Of Values

An analysis is made of the rate of the mass flow through a vacuum seal separating two rarefied gas environments. The determination of the mass throughflow characteristics involves the formulation and solution of a coupled system of six integral equations. The formulation is performed using the methods of kinetic theory. Numerical solutions are carried out for a wide range of values of the seal geometrical parameter. Mass flow results evaluated from these solutions are presented graphically. In addition, representative distributions of the mass fluxes at the participating surfaces are given.

High Resolution Heat Transfer Measurements on the Stator Endwall of an Axial Turbine

2014 ◽  
Author(s):  
Benoit Laveau ◽  
Reza S. Abhari ◽  
Michael E. Crawford ◽  
Ewald Lutum
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
High Resolution ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
Mass Flow ◽  
Wall Temperature ◽  
Adiabatic Wall ◽  
Axial Turbine ◽  
The Heat Transfer Coefficient

In order to continue increasing the efficiency of gas turbines, an important effort is made on the thermal management of the turbine stage. In particular understanding and accurately estimating the thermal loads in a vane passage is of primary interest to engine designers looking to optimize the cooling requirements and ensure the integrity of the components. This paper focuses on the measurement of endwall heat transfer in a vane passage with a 3D airfoil shape and cylindrical endwalls. It also presents a comparison with predictions performed using an in-house developed RANS solver featuring a specific treatment of the numerical smoothing using a flow adaptive scheme. The measurements have been performed in a steady state axial turbine facility on a novel platform developed for heat transfer measurements and integrated to the nozzle guide vane row of the turbine. A quasi-isothermal boundary condition is used to obtain both the heat transfer coefficient and the adiabatic wall temperature within a single measurement day. The surface temperature is measured using infrared thermography through small view ports. The infrared camera is mounted on a robot-arm with six degrees of freedom to provide high resolution surface temperature and a full coverage of the vane passage. The paper presents results from experiments with two different flow conditions obtained by varying the mass flow through the turbine: measurements at the design point (ReCax = 7,2.105) and at a reduced mass flow rate (ReCax = 5,2.105). The heat transfer quantities, namely the heat transfer coefficient and the adiabatic wall temperature, are derived from measurements at 14 different isothermal temperatures. The experimental data are supplemented with numerical predictions that are deduced from a set of adiabatic and diabatic simulations. In addition, the predicted flow field in the passage is used to highlight the link between the heat transfer patterns measured and the vortical structures present in the passage.

Orifice flow at high Knudsen numbers

1961 ◽  
Vol 10 (3) ◽  
pp. 371-384 ◽  
Author(s):  
Roddam Narasimha
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Free Molecule ◽  
First Order ◽  
Orifice Flow ◽  
Flow Through ◽  
The Mean ◽  
Molecule Flow ◽  
Inverse Knudsen Number

Several interesting features of the flow field in free-molecule flow through an orifice are discussed. An estimate is then made of the deviation of the mass flow $\dot{m}$ through the orifice from its limiting free-molecule value $\dot{m}$ for small departures from the limit. Using an iteration method proposed by Willis, it is shown that this deviation is of the first order in ε, the inverse Knudsen number, defined as the ratio of the radius of the hole to the mean free path in the gas at upstream infinity. An estimate of the coefficient is obtained making some reasonable assumptions about the three-dimensional nature of the flow, and the value so derived, giving $\dot{m}=\dot{m}(1+0.25\epsi)$, shows fair agreement with the measurements of Liepmann. It appears that ‘nearly’ free-molecular conditions prevail up to ε ∼ 1.0.

Free Molecule Flow Through Slit and Annular Orifices in the Presence of Participating Bounding Walls

1969 ◽  
Vol 36 (4) ◽  
pp. 715-722
Author(s):  
E. M. Sparrow ◽  
H. S. Yu ◽  
T. S. Lundgren
Keyword(s):  
Integral Equations ◽  
Approximate Model ◽  
Geometrical Parameters ◽  
Free Molecule ◽  
Closed Form Solutions ◽  
Wide Range ◽  
Flow Through ◽  
Bounding Surfaces ◽  
Molecule Flow ◽  
Range Of Values

The effect of actively participating bounding surfaces on the free molecule flow through a slit or an annular orifice situated in a wall separating two regions of different pressure is analyzed. The flow through the slit or orifice depends on the distributions of the flux of mass leaving the bounding surfaces. These distributions are found by formulating and solving pairs of integral equations. In the case of the slit, the integral equations are formulated by employing kinetic theory methods, while for the annular orifice it was found advantageous to use the techniques of radiative transfer. In addition to exact solutions, closed-form solutions based on an approximate model are derived. Results are presented for a wide range of values of the relevant geometrical parameters.

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