Mohammad H. Naraghi

A Model for Design and Analysis of Regeneratively Cooled Rocket Engines

A new model for the design and analysis of a regeneratively cooled rocket engine is developed. In this model two proven rocket thermal analysis codes, TDK and RTE, were conjugated. The integration of these codes was accomplished via an interface file. The accuracy of this combined TDK-RTE model was examined by comparing its results to those of other methods for the SSME and experimental data for a liquid oxygen cooled RP1/LOX engine. Several of the additions and modifications incorporated into this model make it an excellent tool for designing the cooling circuits of regeneratively cooled engines.

Analysis of radiation-natural convection interactions in 1 -g and low-g environments using the discrete exchange factor method

A new numerical method is presented for the analysis of combined natural convection and radiation heat transfer with applications in many engineering situations such as materials processing, combustion and fire research. Because of the recent interest in the low gravity environment of space, attention is devoted to both 1-g and low-g applications. The two-dimensional mathematical model is represented by a set of coupled nonlinear integro-partial differential equations. Radiative exchange is formulated using the Discrete Exchange Factor method (DEF). This method considers point to point exchange and provides accurate results over a wide range of radiation parameters. Numerical results show that radiation significantly influences the flow and heat transfer in both low-g and 1-g applications. In the low-g environment, convection is weak, and radiation can easily become the dominant heat transfer mode. It is also shown that volumetric heating by radiation gives rise to an intricate cell pattern in the top heated enclosure.

A volume radiation heat transfer model for Czochralski crystal growth processes

Thermal modeling of Czochralski (CZ) crystal growth processes is a challenging task owing to the complex interaction of heat conduction, convection, thermal radiation, fluid flow, and other transport phenomena. A highly innovative, general-purpose computer model for phase-change and free-surface problems, utilizing a multi-zone adaptive grid generation and curvilinear finite volume scheme, is linked to a spectral thermal radiation algorithm to predict the temperature distribution within a CZ growth furnace. The radiative transfer model, based on the discrete exchange factor method, is capable of addressing the complexities due to irregularly shaped axisymmetric geometries and shadowing effects. A unified exchange factor model is used to account for multiple reflection/scattering of radiation within the crystal medium. Several numerical trials are performed to simulate the CZ growth of yttrium aluminum garnet. The effect of the top surface boundary condition on temperature profile, crystal/melt interface shape, and process stability is studied to examine the applicability of this model to control the growth conditions and interface shape. The results show that there exists a temperature range for the top surface to avoid the superheating/subcooling of crystal near the interface. This limiting temperature range is, however, dynamic and changes as the growth progresses.

A Continuous Exchange Factor Method for Radiative Exchange in Enclosures with Participating Media

A continuous exchange factor method for the analysis of radiative exchange in gray enclosures with absorbing-emitting and isotropically scattering media and diffuse surfaces is developed. In this method two type of exchange function are defined: the direct exchange function and the total exchange functions are developed. These integral equations are solved using a Gaussian quadrature integration method. The results obtained based on the present approach are found to be more accurate than those of the zonal method. Unlike the zonal method, in the present approach, there is no need for evaluation of multiple integrations for calculating direct exhange factors.

Gravitational and centrifugal buoyancy effects in curved square channels with conjugated boundary conditions

Abstract Fully developed laminar flow in a curved square channel with peripheral wall conduction is examined. The wall average Nusselt number, Nu , is presented as a function of four parameters: the wall conduction parameter, φ, the Prandtl number, and two Grashof numbers, Grg and Grc, which represent the gravitational and centrifugal forces, respectively, present in a variable density fluid. Numerical solutions are presented for 4.4 Nu values are demonstrated to be reduced below the curved channel forced convection values due to a weakening of the secondary flow field. A curve illustrating the relationship between φeff, defined as the value of φ at which a constant wall temperature boundary condition can be assumed, and De is presented.

A unified matrix formulation for the zone method: a stochastic approach

Abstract A new approach based on the Markov chain theory is utilized to derive three explicit matrix relations for the total exchange areas of the zone method. These relations are identical to those published earlier. The same method is used to derive a single explicit matrix relation for the total exchange areas. This expression is so general that it covers the same function as the aforementioned relations.

A Stochastic Approach for Radiative Exchange in Enclosures With Nonparticipating Medium

A stochastic method is developed for calculating radiation interchange in enclosures with a finite number of isothermal surfaces but without a participating medium. Different types of surface properties are considered. They are diffuse and specular surfaces. In this work, a stochastic n model is proposed that is based on the Markov chain theory and leads to some explicit matrix relationships for the absorption factor from which the heat transfer characteristics of the enclosure can be determined. The present approach provides an exact solution as long as the necessary view factors can be determined. The accuracy of approximate solutions can be improved as n increases.

A CFD-RTE Model for Thermal Analysis of Regeneratively Cooled Rocket Engines

This paper presents a computational methodology for thermal analysis of hot-gas-side and coolant–side of regeneratively cooled liquid rocket engines. The computational methodology is composed of a CFD model, for the hot-gas-side and RTE (Rocket Thermal Evaluation) for the coolant flow and wall conduction. The CFD model solves the axisymmetric flow and thermal fields of hot-gas in the thrust chamber and nozzle. The RTE predicts the coolant side properties and the wall temperature distribution. This integrated CFD-RTE model is validated by comparing its results with the published data for the space shuttle main engine (SSME). Nomenclature A r = surface area vector f A r = area of face f faces N = number of faces enclosing cell φ S = source of φ per unit volume V = cell volume φ

Radiative transfer in arbitrarily-shaped axisymmetric enclosures with anisotropic scattering media

Abstract Two numerical models for solving thermal radiative transport in irregularly-shaped axisymmetric bodies containing a homogeneous, anisotropically scattering medium are presented. The N -bounce method approximates total exchange factors by summing direct and user-designated higher order terms representative of multiple reflections/scattering. The source function approach is an intensity-based method relating the source function (gas leaving intensity) to the surface leaving intensity. Both methods are based on the Discrete Exchange Factor method, where exchange factors between arbitrarily-oriented differential surface and/or volume elements are calculated in a straightforward approach. The present methods are capable of addressing blockage effects produced by inner and/or outer blocking bodies. The results obtained via the current methods are found to be in good agreement with the existing solutions to several axisymmetric benchmark problems. The solutions to several two-dimensional axisymmetric problems are presented.

NUMERICAL MODEL FOR RADIATIVE HEAT TRANSFER ANALYSIS IN ARBITRARILY SHAPED AXISYMMETRIC ENCLOSURES WITH GASEOUS MEDIA

A numerical model is presented for evaluating thermal radiative transport in irregularly shaped axisymmetric enclosures containing a homogeneous, isotropically scattering medium. Based on the discrete exchange factor (DEF) method, exchange factors between arbitrarily oriented differential surface/volume ring elements are calculated using a simple approach. The present method is capable of addressing blockage effects produced by inner/outer obstructing bodies. The results obtained via the current method are found to be in excellent agreement with existing solutions to several cylindrical media benchmark problems. The solutions to several rocket-nozzle and plug-chamber geometries are presented for a host of geometric conditions and optical thicknesses.