Richard J Goldstein

Bio: Richard J Goldstein is an academic researcher from University of Minnesota. The author has contributed to research in topics: Heat transfer & Heat transfer coefficient. The author has an hindex of 56, co-authored 242 publications receiving 14047 citations. Previous affiliations of Richard J Goldstein include University of Illinois at Chicago & Tulane University.

Local Heat Transfer to Staggered Arrays of Impinging Circular Air Jets

Abstract: Measurements are made of the local heat transfer from a flat plate to arrays of impinging circular air jets. Fluid from the spent jets is constrained to flow out of the system in one direction. Two different jet-to-jet spacings, 4 and 8 jet diameters, are employed. The parameters that are varied include jet-orifice-plate to impingement-surface spacing and jet Reynolds number. Local heat transfer coefficients vary periodically both in the flow direction and across the span with high values occurring in stagnation regions. Stagnation regions of individual jets as determined by local heat transfer coefficients move further in the downstream direction as the amount of crossflow due to upstream jet air increases. Local heat transfer coefficients are averaged numerically to obtain spanwise and streamwise-spanwise averaged heat transfer coefficients.

Laminar natural convection from a horizontal plate and the influence of plate-edge extensions

Abstract: Laminar natural convection from a horizontal plate is studied by a finite-difference analysis and by experiments for Rayleigh numbers from 10 to 104. The plate with uniform surface temperature or concentration on one side and insulated on the other is situated in an ‘infinite’ fluid medium. The buoyancy near the surface is directed either outward or inward normal to the active surface – equivalent to a heated plate facing upward or downward. The effect of insulated vertical and horizontal extensions to the plate are also examined.Finite-difference solutions are obtained for a heated strip in a two-dimensional domain for a Prandtl number of 0·7. Mass-transfer experiments are performed with square naphthalene plates in air. Both numerical and experimental results justify a 1/5-power law in the present range of Rayleigh number – i.e. Nusselt number or Sherwood number proportional to the Rayleigh number raised to the 1/5 power. The horizontal extensions cause a limited reduction in the transfer rate for the plate generating ‘outward buoyancy’, and a larger reduction with ‘inward buoyancy’. The vertical walls block the fluid flow directly, and thus greatly lower the transfer rate with either outward or inward buoyancy.

The Influence of Curvature on Film Cooling Performance

Abstract: The effects of injection rate and strength of curvature on film cooling performance of gas injected through a row of holes on a convex surface is studied. Comparisons are made to film cooling of concave and flat surfaces. Three different relative strengths of curvature (ratio of radius of curvature to radius of injection hole), two density ratios (0.95 and 2.0), and a wide range of blowing rates (0.3 to 2.7) are considered. A foreign gas injection technique (mass transfer analogy) is used. The strength of curvature was controlled by varying the injection hole diameter. At low blowing rates, film cooling is more effective on the convex surface than on a flat or a concave surface. The cross stream pressure gradient present in curved flows tends to push the jet into the convex wall. As the injection rate is increased, normal and tangential jet momentum promote lift-off from the convex surface, thereby lowering performance. In contrast, previous studies show that on a concave surface, tangential jet momentum, flow instabilities, and blockage improve performance on a concave surface as blowing rate is increased.Copyright © 1990 by ASME

Film cooling downstream of a row of discrete holes with compound angle

Abstract: A special naphthalene sublimation technique is used to study the film cooling performance downstream of one row of holes of 35° inclination angle and 45° compound angle with 3 diameter hole spacing and relatively small hole length to diameter ratio (63) Both film cooling effectiveness and mass/heat transfer coefficients are determined for blowing rates from 05 to 20 with density ratio of unity The mass transfer coefficient is measured using pure air film injection, while the film cooling effectiveness is derived from comparison of mass transfer coefficients obtained following injection of naphthalene-vapor-saturated air with that of pure air injection This technique enables one to obtain detailed local information on film cooling performance General agreement is found in local film cooling effectiveness when compared with previous experiments The laterally-averaged effectiveness with compound angle injection is higher than that with inclined holes immediately downstream of injection at a blowing rate of 05 and is higher at all locations downstream of injection at larger blowing rates A large variation of mass transfer coefficients in the lateral direction is observed in the present study At low blowing rates of 05 and 10, the laterally-averaged mass transfer coefficient is close to that of injection without compound angle At the highest blowing rate used (20), the asymmetrical vortex motion under the jets increases the mass transfer coefficient drastically ten diameters downstream of injectionCopyright © 2000 by ASME

Pattern formation outside of equilibrium

Abstract: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

Experimental and Theoretical Investigation of Backward-Facing Step Flow

Abstract: Laser-Doppler measurements of velocity distribution and reattachment length are reported downstream of a single backward-facing step mounted in a two-dimensional channel. Results are presented for laminar, transitional and turbulent flow of air in a Reynolds-number range of 70 < Re < 8000. The experimental results show that the various flow regimes are characterized by typical variations of the separation length with Reynolds number. The reported laser-Doppler measurements do not only yield the expected primary zone of recirculating flow attached to the backward-facing step but also show additional regions of flow separation downstream of the step and on both sides of the channel test section. These additional separation regions have not been previously reported in the literature.Although the high aspect ratio of the test section (1:36) ensured that the oncoming flow was fully developed and two-dimensional, the experiments showed that the flow downstream of the step only remained two-dimensional at low and high Reynolds numbers.The present study also included numerical predictions of backward-facing step flow. The two-dimensional steady differential equations for conservation of mass and momentum were solved. Results are reported and are compared with experiments for those Reynolds numbers for which the flow maintained its two-dimensionality in the experiments. Under these circumstances, good agreement between experimental and numerical results is obtained.

Turbulent flows over rough walls

Abstract: ▪ AbstractWe review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number ks+, which measures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low ks+ depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with δ/k ≲ 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness element...