Monograph records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 18:10:35 +0000Investigation of the Stability of the Laminar Boundary Layer in a Compressible Fluid
https://resolver.caltech.edu/CaltechAUTHORS:LEEnacatn1115
Authors: Lees, Lester; Lin, Chia Chiao
Year: 1946
In the present report the stability of two-dimensional laminar flows of a gas is investigated by the method of small perturbations. The chief emphasis is placed on the case of the laminar boundary layer.
Part I of the present report deals with the general mathematical theory. The general equations governing one normal mode of the small velocity and temperature disturbances are derived and studied in great detail. It is found that for Reynolds numbers of the order of those encountered in most aerodymnic problems, the temperature disturbances have only a negligible effect on those particular velocity solutions which depend primarily on the viscosity coefficient ("viscous solutions"). Indeed, the latter are actually of the same form in the compressible fluid as in the incompressible fluid, at least to the first
approximation. Because of this fact, the mathematical analysis is greatly simplified. The final equation determining the characteristic values of the stability problem depends on the "inviscid solutions" and the function of Tietjens in a manner very similar to the case of the incompressible fluid. The second viscosity coefficient and the coefficient of heat conductivity do not enter the problem; only the ordinary coefficient of viscosity near the solid surface is involved.
Part II deals wlth the limiting case of infinite Reynolds numbers. The study of energy relations is very much emphasized. It is shown that the disturbance will gain energy from the main flow if the gradient of the product of mean density and mean vorticity near the solid surface has a sign opposite to that near the outer edge of the boundary layer.
A general stability criterion has been obtained in terms of the gradient of the product of density and vorticity, analogous to the Rayleigh-Tollmien criterion for the case of an incompressible fluid. If this gradient vanishes for some value of the velocity ratio of the main flow exceeding 1 - 1/M (where M is the free stream Mach number), then neutral and self-excited "subsonic" disturbances exist in the inviscid fluid. (The subsonic disturbances die out rapidly with distance from the solid surface.) The conditions for the existence of other types of disturbance have not yet been established to this extent of exactness. A formula has been worked out to give the amplitude ratio of incoming and reflected sound waves.
It is found in the present investigation that when the solid boundary is heated, the boundary layer flow is destabilized through the change in the distribution of the product of density and vorticity, but stabilized through the increase of kinematic viscosity near the solid boundary. When the solid boundary is cooled, the situation is just the reverse. The actual extent to which these two effects counteract each
other can only be settled by actual computation or some approximate estimstes of the minimum critical Reylolds number. This question will be investigated in a subsequent report.
Part III deals with the stability of laminar flows in a perfect gas with the effect of viscosity included. The method for the numerical computation of the stability limit is outlined; detailed numerical calculations will be carried out in a subsequent report.https://authors.library.caltech.edu/records/x2tja-rc845A Discussion of the Application of the Prandtl-Glauert Method to Subsonic Compressible Flow over a Slender Body of Revolution
https://resolver.caltech.edu/CaltechAUTHORS:LEEnacatn1127
Authors: Lees, Lester
Year: 1946
The Prandtl-Glauert method for subsonic potential flow of a compressible fluid has generally been believed to lead to an increase in the pressures over a slender body of revolution by a factor 1/([sqrt](1-M[sub]1^2)) (where M[sub]1 is Mach number in undisturbed flow) as compared with the pressures in incompressible flow. Recent German work on this problem has indicated, however, that the factor 1/([sqrt](1-M[sub]1^2)) is not applicable in this case. In the present discussion a more careful application of the
Prandtl-Glauert method to three-dimensional flow gives the following results:
The Prandtl-Glauert method does not lead to a universal velocity or pressure correction formula that is independent of the shape of the body. The factor 1/([sqrt](1-M[sub]1^2)) is applicable only to the case of two-dimensional flow.
The increase with Mach number of the pressures over a slender body of revolution is much less rapid than for a two-dimensional airfoil. An approximate formula from which the increase can be estimated is derived theoretically.
The increase with Mach number of the maximum axial interference velocity on a slender body of revolution in a closed wind tunnel is given approximately by the factor 1/((1-M[sub]1^2)^-3/2), rather than by the factor 1/([sqrt](1-M[sub]1^2)) previously obtained by Goldstein and Young and by Tsien and Lees.https://authors.library.caltech.edu/records/get29-pt673The Stability of the Laminar Boundary Layer
https://resolver.caltech.edu/CaltechAUTHORS:LEEnacarpt876
Authors: Lees, Lester
Year: 1947
The present papcr is a continuation of a theoretical investigation of the stability of the laminar boundary layer in a compressible fluid. An approximate estimate for the minimum critical Reynolds number Re[sub]cr[sub-sub]min, or stability limit, is obtained in terms of the distribution of the kinematic viscosity and the product of the mean density [rho][super][bar]* and mean vorticity [formula] across the
boundary layer. With the help of this estimate for Re[sub]cr[sub-sub]min it is shown that withdrawing heat from the fluid through the solid surface increases RRe[sub]cr[sub-sub]min and stabilizes the flow, as compared with the flow over an insulated surface at the same Mach number. Conduction of heat to the fluid through the solid surface has exactly the opposite effect. The value of Re[sub]cr[sub-sub]min for the insulated surface decreases as the Mach number increases for the case of a uniform free-stream velocity. These general conclusions are supplemented by detailed calculations of the curves of wave number (inverse wave length) against Reynolds number for the neutral disturbances for 10 representative cases of insulated and noninsulated surfaces.
So far as laminar stability is concerned, an important difference exists between the case of a subsonic and supersonic free-stream velocity outside the boundary layer. The neutral boundary-layer disturbances that are significant for laminar stability die out exponentially with distance from the solid surface; therefore, the phase velocity c* of these disturbances is subsonic relative to the free-stream velocity [symbol] or [symbol], [symbol] where is the local sonic velocity. When [symbol]<1, (where M[sub]0 is free-stream Mach number), it follows that [inequalities] and any laminar boundary-1ayer flow is ultimately unstable at sufficiently high Reynolds numbers because of the destabilizing action of viscosity near the solid surface, as
explained by Prandtl for the incompressible fluid. When M[sub]0 >1, however, [inequalities]. If the quantity [forumla] is large enough negatively, the rate at which energy passes from the disturbance to the mean flow, which is proportional to [formula], can always be large enough to counterbalance the rate at which energy passes from the mean flow to the disturbance because of the destabilizing action of viscosity near the solid surface. In that case only damped disturbances exist and the laminar boundary layer is completely stable at all Reynolds numbers. This condition occurs when the rate at which heat is withdrawn from the fluid through the solid surface reaches or exceeds a critical value that depends only on the Mach number and the properties of the gas. Calculations show that for M[sub]0 > 3 (approx.) the laminar boundary-layer flow for thermal equilibrium -- where the heat conduction through the solid surface balances the heat radiated from the surface -- is completely stable at all Reynolds numbers under free-flight
conditions if the free-stream velocity is uniform.
The results of the analysis of the stability of the laminar boundary layer must be applied with care to discussions of transition; however, withdrawing heat from the fluid through the solid surface, for example, not only increases Re[sub]cr[sub-sub]min but also decreases the initial rate of amplification of the self-excited disturbances, which is roughly proportional fo 1/[sqrt]Re[sub]cr[sub-sub]min. Thus, the effect of the thermal conditions at the solid sufice on the transition Reynolds number Re[sub]tt, is similar to the effect on Re[sub]cr[sub-sub]min. A comparison between this conclusion and experimental investigations of the effect of surface heating on transition at low speeds shows that the results of the present paper give the proper direction of this effect.
The extension of the results of the stability analysis to laminar boundary-layer gas flows with a pressure gradient in the direction of the free stream is discussed.https://authors.library.caltech.edu/records/e6ywd-87995Time factors in slowing down the rate of growth of demand for primary energy in the United States
https://resolver.caltech.edu/CaltechEQL:EQL-R-7
Authors: Lees, Lester; Lo, Mingin Philip
Year: 2007
DOI: 10.7907/Z9W37T8G
The purpose of this report is to identify the time scales involved in slowing down the rate of growth of primary energy consumption in the U.S., as one component of an overall energy/environment strategy designed to limit the required volume of energy imports from overseas. Two important energy-consuming sectors of the economy are chosen as illustrative examples: (1) the "automobile" as a total system (25%); (2) space heating, air conditioning and water heating in the residential sector (22%). Efficient, light-weight vehicles are introduced into the automobile population by allocating an increasing percentage of new car production to such vehicles year by year until some fixed percentage is attained. Parametric calculations show that significant reductions in the annual rate of energy consumption by automobiles can be achieved if (a) the fuel consumption of efficient vehicles is 60% or less of "standard" vehicles; (b) the increment in percentage of new car production devoted to efficient vehicles is not less than 8% per year; (c) the efficient vehicles are "frozen" at not less than 80% or more of all new car production at the end of an eight to ten year period. In the residential sector the "turnover" rate is comparatively low, and the calculated reduction in annual energy growth rate produced by energy-conserving measures is modest, as expected, unless a "retrofit" rate of older living units of at least 2% per year can be attained.
These two components of an energy-conserving policy taken together would bring the growth rate in U. S. primary energy demand down from its present rate of 4.2% per year to about 2.8% per year by 1985. Reductions in the annual growth rate of the remaining 50% of U.S. primary energy consumption that seem quite feasible would bring the overall growth rate down to about 2.5% per year by 1985. If reductions in growth rate of this magnitude could in fact be achieved, energy imports would peak in the mid-1980s at a level no higher than about 60% above the present (1973) volume of imports. Incentives and disincentives designed to bring about this slowdown in the rate of U. S. energy consumption are discussed briefly.https://authors.library.caltech.edu/records/k0154-nkk36People, power and pollution: environmental and public interest aspects of electric power plant siting
https://resolver.caltech.edu/CaltechEQL:EQL-R-1
Authors: Borrelli, Peter; Lees, Lester; Easterling, Mahlon; Pauker, Guy; Klein, Burton H.; Poppe, Robert
Year: 2007
DOI: 10.7907/Z9TD9V7P
Explanatory Note:
On March 16, 1971, the National Academy of Engineering convened the Forum of the Committee on Power Plant Siting (COPPS) in Washington, D.C. After two days of plenary sessions the members of the three main working groups met for three days to begin drafting their reports. Four of the authors of the present report (Borrelli, Easterling, Lees and Poppe) constituted the sub-group on Environmental Aspects of Siting of Working Group II-Systems Approach to Site Selection. Intensive discussions in Washington in this sub-group, and the subsequent exchange of draft sections by mail, convinced us that we should go far beyond our original assignment and probe into all aspects of power plant siting, especially the public interest factors. During a second intensive working session in Pasadena, California, on April 22 and 23, 1971, we were joined by Guy Pauker and Burton H. Klein, who also participated in the subsequent redrafting of the final report. We are grateful to the NAE-COPPS for stimulating our thinking on this important and difficult problem. However, the final report is solely our responsibility as individuals and the responsibility of the Caltech Environmental Quality Laboratory.
Lester Lees
Director, Environmental Quality Laboratoryhttps://authors.library.caltech.edu/records/rrk5j-53w74Implications of the growth in demand for commercial and industrial electrical energy in the South Coast Air Basin
https://resolver.caltech.edu/CaltechEQL:EQL-R-2
Authors: Lees, Lester
Year: 2007
DOI: 10.7907/Z98913SQ
An examination of statistical data for the period 1960-1970 shows a simple correlation between the growth in demand for commercial electrical energy in the South Coast Air Basin and the growth in commercial floor area and in electrical loading per square foot. Demand for industrial electrical energy correlates strongly with value added by manufacture and with kilowatt-hours per dollar of value added; growth in manufacturing floor area is a secondary factor. These simple correlations are utilized to forecast future demand for electrical energy in the Basin in terms of plausible "minimum" and "maximum" rates of economic growth. Comparisons between these demand projections and conservative estimates of available electrical generating capacity bring out the "tightness" of the short-run demand-supply situation. A "management standard" for growth in demand for electrical energy of 5% per year is suggested as a goal for the mid-1970's. Long-range implications of environmental, land use and technological constraints on electrical energy supply are examined and related to possible limitations on the rate of economic expansion in the South Coast Air Basin. Conversely, one can utilize the results of this study to estimate the relationship between a desired rate of economic growth and the demand for electrical energy.https://authors.library.caltech.edu/records/t9zbq-7at93Smog: a report to the people
https://resolver.caltech.edu/CaltechEQL:EQL-R-4
Authors: Lees, Lester; Braly, Mark; Easterling, Mahlon; Fisher, Robert; Heitner, Kenneth; Henry, James; Horne, Patricia J.; Klein, Burton; Krier, James; Montgomery, W. David; Pauker, Guy; Rubenstein, Gary; Trijonis, John
Year: 2007
DOI: 10.7907/Z93B5X30
The Environmental Quality Laboratory (EQL) traces its origins to a series of discussions initiated by Caltech President Harold Brown on the feasibility of a Caltech Air Pollution Laboratory aimed at alleviating the smog problem in the South Coast Air Basin. In an address to the Institute for the Advancement of Engineering on February 28, 1970, [1] Dr. Brown summarized the main conclusions of a faculty-JPL study group on smog led by Professor Carver Mead that preceded the formation of the EQL. To quote from Dr. Brown's address, the most important conclusion "is that there are other factors which are as important or more important than the technological ones.... Unless expert social scientists are available -- and I mean not only economists to examine the economic balance, but political scientists, sociologists, psychologists, and so on -- the study will be done in too narrow a context. Although it will give the right answers to its own questions, it will prove to have overlooked questions more important than those which it asked."
Our experience in working on the smog problem over the past year fully confirms Dr. Brown's observations. The EQL team engaged in this study included social scientists, lawyers, engineers, and graduate and undergraduate students. Each of us had to learn that the social, cultural, legal, economic and technical factors interact strongly and therefore cannot be treated separately. In addition to innumerable internal debates, seminars and memos, we had the benefit of numerous discussions with people in industry, in environmental action groups, and in government at all levels who are concerned with air pollution.
At the outset of the EQL study we made the decision to consider only those air pollution control strategies that comply with the spirit (if not the letter) of the Clean Air Act of 1970. In the spirit of that act this report describes a "management standards" approach for achieving drastic reductions in the number of "smoggy" days in the South Coast Air Basin of California by the end of 1977. In order to illustrate the kinds of control measures that are required if the management air quality standards are to be satisfied, we chose one particular control strategy for detailed study. This strategy, called EQL Strategy # 1, is based on new "technical" control measures on stationary sources and used motor vehicles, combined with a set of social and economic incentives and disincentives designed to encourage the shift to low-pollution motor vehicles, to encourage the use of multiple-occupancy vehicles (buses, carpools, etc.), and to halt or at least reduce the annual rate of increase in gasoline consumption in the Basin. [2] If EQL Strategy # 1 is followed, we estimated that the average number of days per year on which the California ambient air quality standard on photochemical oxidants is violated would be reduced from 241 days in 1970 to 50 days by the end of 1975, and to 25 days by the end of 1977.
The measures we propose are neither painless not inexpensive. We did not find any "magic solutions." For example, the cost of EQL Strategy # 1 for this Basin is estimated at about one billion dollars through the end of 1975, or about $100 per head. Whether or not the results that could be achieved are worth the effort and expense is up to the people of the South Coast Air Basin to decide.
An earlier version of this report called EQL Report # 4, dated January 15, 1972, consisted of Part I, which contained a summary of EQL Strategy 1, and Part II, which briefly outlined the legislative and administrative actions required. The present final edition of the EQL air pollution report contains a revised and updated version of Part I and a new Part II, entitled "Supporting Information and Analysis."
Our work on the short-term (1972-1977) air pollution control problem raised important and difficult questions about the long-range (1982-2000) problem of controlling air pollution in the South Coast Air Basin. Members of the EQL staff are studying new technologies, social and economic incentives, modes of transportation and patterns of land use and development in an attempt to formulate a long-range strategy.
Lester Lees
Director, Environmental Quality Laboratory
Pasadena, California
June 15, 1972
[1] Brown, H.: "The University and Environmental Research," Bulletin of the California Institute of Technology, Vol. 79, No. 1, March 7, 1970.
[2] Some of these technical control measures are also included in the Implementation Plan submitted by the State to the U.S. Environmental Protection Agency in February, 1972.https://authors.library.caltech.edu/records/2z9px-ffs97State Power Plant Siting: a Sketch of the Main Features of a Possible Approach
https://resolver.caltech.edu/CaltechEQL:EQL-M-4
Authors: Krier, James E.; Lees, Lester; Dawes, Daniel
Year: 2009
DOI: 10.7907/Z9ZC80S1
Work on various phases of power plant technology and siting has been underway within the Environmental Quality Laboratory (EQL) at the California Institute of Technology for some time. Of particular relevance to this memorandum, a good deal of effort has been devoted to institutional aspects of the siting process. Our purpose in what follows is to draw from our past work -- and from the discussions and work of others -- a sketch of the major outlines of one possible approach to power plant siting for the state. We hope in doing so to give our present views about the issues and how they might rationally be resolved, not so much to convince as to inform, stimulate fruitful ideas, and help provide the basis for constructive debate. We ourselves are not necessarily wedded to any of the discussion that follows; we find our own minds changing from time to time as we study the problem further or confront sound suggestions from others.
Part I of this memorandum briefly outlines the major features of what we see as a fruitful approach to the siting problem. Sections A through E of Part I describe some elements of the approach; Section F sketches the actual siting decision process we suggest, and in doing so shows how the elements play into the process. Section G comments briefly on a suggested role for judicial review.
In Part II we attempt to reduce our ideas to a fairly precise outline for a state siting statute, and to deal with certain matters of detail not covered in Part I. Section A of Part II introduces the statutory outline by summarizing each of its provisions; Section B sets forth the outline itself. The Appendix to this memorandum depicts our suggested approach in time-line fashion; it should be helpful in reading and understanding the proposal.https://authors.library.caltech.edu/records/hkx6g-vm495Emissions and air quality trends in the South Coast Air Basin
https://resolver.caltech.edu/CaltechEQL:EQL-M-16
Authors: Trijonis, John C.; Peng, Ted K.; McRae, Gregory J.; Lees, Lester
Year: 2009
DOI: 10.7907/Z9J67DWH
This paper documents the historical trends of pollutant emissions and ambient air quality for the South Coast Air Basin (SCAB) for the period 1965-1974. Emission trends for nitrogen oxides. reactive hydrocarbons, and carbon monoxide are developed. A detailed appendix describes the methodology and presents the latest test information -- in particular the contribution of evaporative emissions from light-duty vehicles. Basin-wide and county trends are presented to characterize the overall changes as well as the spatial distribution of emissions. Ambient concentrations of total nitrogen oxides (NO_x), nitrogen dioxide (NO_2), oxidant (OX), and carbon monoxide (CO) are compared to the emissions changes during the same period. Detailed analyses of air quality indices, including extreme levels, average values. and frequency of standard violation are presented for each pollutant. The final section of the paper discusses current and proposed control strategies and their impact on future air quality.https://authors.library.caltech.edu/records/serfy-vn655Plane Couette Flow at Low Mach Number According to the Kinetic Theory of Gases
https://resolver.caltech.edu/CaltechAUTHORS:20150604-152209034
Authors: Yang, Hsun-Tiao; Lees, Lester
Year: 2015
The thirteen-moment approximation developed by H. Grad
for solving the Maxwell-Boltzmann equation is applied to the problem of the relative shearing motion between two infinite, parallel flat plates (plane Couette flow). In order to bring out the molecular effects as directly as possible the problem is linearized by requiring
that the Mach number is small compared with unity, and that the temperature difference between the two plates is small compared with ambient temperature. According to the linearized Grad equations the shear stress in this case is given by the usual Navier-Stokes relation for all values of the parameter Re/M, in agreement with R. A.
Millikan's postulate. Also the linearized boundary conditions for this problem are identical with the Maxwell slip relations utilized by Millikan, so the same expressions for slip velocity and drag coefficient
are obtained. An examination of the drag data obtained by Kuhlthau, Chiang, and Bowyer and Talbot in their rotating-cylinder experiments at low densities shows that the variation of 1/C_DM with Re/M is predicted reasonably well by this theory over a range of Mach numbers
from 0.15 to 1.40, in spite of the fact that the theory is supposed to hold only for low Mach numbers.https://authors.library.caltech.edu/records/yge61-bnq32A Kinetic Theory Description of Rarefied Gas Flows
https://resolver.caltech.edu/CaltechAUTHORS:20151102-150954032
Authors: Lees, Lester
Year: 2015
An approach to the kinetic theory of gas flows is developed which starts with Maxwell's original integral equations of transfer, rather than with the Maxwell-Boltzmann equation for the velocity distribution function itself. In this procedure the Maxwell-Boltzmann equation is satisfied in
a certain average sense, rather than at every point. The advantage of this method is that relatively simple distribution functions are utilized which contain a small number of unknown functions to be determined by
applying the conservation laws, plus several additional higher moments. For simplicity a "two-stream Maxwellian" is employed, which is a natural extension and generalization of Mott-Smith's function for a normal shock,
but differs from it in certain essential respects. As an illustration, the method is applied to linearized plane Couette flow and Rayleigh's problem. Reasonable results are obtained for macroscopic quantities such as mean
velocity and shear stress over the whole range of densities from free-molecule flow to the Navier-Stokes regime. This technique is now being applied to some typical non-linear rarefied gas flows.https://authors.library.caltech.edu/records/16bsm-49w92Kinetic Theory Description of Plane, Compressible Couette Flow
https://resolver.caltech.edu/CaltechAUTHORS:20151104-163525738
Authors: Lees, Lester; Liu, Chung-Yen
Year: 2015
By utilizing the two-stream Maxwellian in Maxwell's integral
equations of transfer we are able to find a closed-form solution of the problem of compressible plane Couette flow over the whole range of gas density from free molecule flow to atmospheric. The ratio of shear
stress to the product of ordinary viscosity and velocity gradient, which is unity for a Newtonian fluid, here depends also on the gas density, the
plate temperatures and the plate spacing. For example, this ratio decreases rapidly with increasing plate Mach number when the plate temperatures are fixed. On the other hand, at a fixed Mach number based on the temperature of one plate, this ratio approaches unity as
the temperature of the other plate increases. Similar remarks can be made for the ratio of heat flux to the product of ordinary heat conduction
coefficient and temperature gradient.
The effect of gas density on the skin friction and heat transfer coefficients is described in terms of a single rarefaction parameter, which amounts to evaluating gas properties at a certain "kinetic temperature"
defined in terms of plate Mach number and plate temperature ratio. One interesting result is the effect of plate temperature on velocity "slip".
In the Navier-Stokes regime most of the gas follows the hot plate, because the gas viscosity is larger there. As the gas density decreases the situation is reversed, because the velocity slip is larger at the hot plate
than at the cold plate. In the limiting case of a highly rarefied gas most of the gas follows the cold plate.https://authors.library.caltech.edu/records/e7be0-4zg83Kinetic Theory Description of Conductive Heat Transfer from a Fine Wire
https://resolver.caltech.edu/CaltechAUTHORS:20151105-155638313
Authors: Lees, Lester; Liu, Chung-Yen
Year: 2015
The Maxwell moment method utilizing the two-sided Maxwellian
distribution function is applied to the problem of conductive heat transfer between two concentric cylinders at rest. Analytical solutions are obtained for small temperature differences between the cylinders.
The predicted heat transfer agrees very well with experiments performed by Bomelburg, Schäfer-Rating and Eucken. Comparison with results given by Grad's thirteen moment equations, and with those given by Fourier's "law" plus the Maxwell-Smoluchowski temperature-jump
boundary condition shows that the two-sided character in the
distribution function is a crucial factor in problems involving surface curvature.https://authors.library.caltech.edu/records/xgm4e-w1v24Some Remarks on Integral Moment Methods for Laminar Boundary Layers with Application to Separation and Reattachment
https://resolver.caltech.edu/CaltechAUTHORS:20151124-143821828
Authors: Lees, Lester; Reeves, Barry L.
Year: 2015
It is well known that the Kármán-Pohlhausen integral method
is a rather poor approximation for the analysis of laminar boundary layers in regions of adverse pressure gradient, particularly when separation occurs. Perhaps not so well known, however, is the fact that the Kármán-Pohlhausen method may be completely inadequate downstream of separation, between the separation and reattachment
points. When a flow disturbance, such as a forward facing step or incident shock wave, is of sufficient strength to cause extensive separation, the static pressure variation along the surface takes the general appearance shown in Figure 1. The region where the static pressure is virtually constant (plateau) gives rise to much of the
difficulty, since the Kármán-Pohlhausen method must produce an attached, Blasius type velocity profile whenever the pressure gradient vanishes. Hence the Kármán-Pohlhausen method must predict reattachment upstream of the plateau, whereas in reality it occurs downstream
of the plateau. Apparently what is needed is an integral method which exhibits velocity profiles containing reverse-flow for vanishingly small adverse pressure gradients analogous to the "lower branch"
solutions of the Falkner-Skan equation, which were found by Stewartson. The purpose of the present report is to demonstrate that the method first proposed by Walz
and modified by Tani does indeed produce
velocity profiles with reverse flow, even in the limit of constant pressure, and would, therefore, appear to be a very promising method for predicting the behavior of separated flows. Furthermore this method
eliminates the need for a certain amount of empiricism inherent in other existing methods, such as is required at the present time with the Crocco-Lees theory.https://authors.library.caltech.edu/records/njzvj-g4779Finite Disturbance Effect on the Stability of a Laminar Incompressible Wake Behind a Flat Plate
https://resolver.caltech.edu/CaltechAUTHORS:20151201-133700798
Authors: Ko, Denny R. S.; Kubota, Toshi; Lees, Lester
Year: 2015
An integral method is used to investigate the interaction
between the stability of a single frequency finite amplitude disturbance with the non-parallel mean flow in a laminar, incompressible wake behind a flat plate. The mean flow is assumed to be characterized by a few shape parameters. The integrals involving the fluctuating
components are determined as functions of those shape parameters by solving the inviscid Rayleigh equation of the linear stability theory using the local mean flow. The variations of the amplitude of the fluctuation and the mean flow in the streamwise direction are then determined from solving the set of ordinary differential equations.
The effect of coupling between the mean flow and the fluctuation was found to be very important. The calculations show good agreement with the experimental data of Sato and Kuriki.https://authors.library.caltech.edu/records/7adrv-phr25Inviscid Hypersonic Flow Over Blunt-Nosed Slender Bodies
https://resolver.caltech.edu/CaltechAUTHORS:20151203-165813194
Authors: Lees, Lester
Year: 2015
At hypersonic speeds the drag/area of a blunt nose is much larger than the drag/area of a slender afterbody, and the energy contained in the flow field in a plane at right angles to the flight direction is nearly constant over a downstream distance many times greater than the characteristic nose dimension. The transverse flow field exhibits certain similarity properties directly analogous to the flow similarity behind an intense blast wave found by G. I. Taylor and S. C. Lin. Conditions for constant energy show that the shape of the bow shock wave R(x) not
too close to the nose is given by R/d = K_1 (γ)(d/c)^(1/2) for a body of revolution, and by R/d = K_0(γ) (x/d)^(2/3) for a planar body, where d is nose diameter, or leading-edge thickness. A comparison with the experiments of Hammitt, Vas, and Bogdonoff on a flat plate with a blunt leading-edge at M_∞ = 13 in helium shows that the shock wave shape is predicted very accurately by this analysis. The predicted surface pressure distribution is somewhat
less satisfactory.
Energy considerations combined with a detailed study of the
equations of motion show that flow similarity is also possible for a class of bodies of the form r_b ~ x^m, provided that m' ≤ m ≤ 1, where m' = 3/4 for a planar body and m' = (3/2(γ+1))/(3γ + 2) for a body of revolution. When m < m' the shock shape is not similar to the body shape, and except for the constant energy flows the entire
flow field some distance from the nose must depend to some extent on the details of the nose geometry.
Be again again utilizing energy and drag considerations one finds that at hypersonic speeds the inviscid surface pressures generated by a blunt nose are larger than the pressures produced by boundary layer growth on a flat surface over a distance from the nose of order ℓ, where
ℓ/d ≃ 1/15 ((Re_d)/M_∞^2))^3 (Here Re_d is free-stream Reynolds number based on leading-edge thickness.)
Thus at M_∞ = 15 the viscous interaction effects should be important for Re_d < 10^3, but somewhere in the range 1500 < Re_d < 2000 the inviscid effects must spread rapidly over the plate surface, and certainly for Re_d > 3000 the inviscid pressure field is dominant and determines
the boundary layer development, skin friction and heat transfer over the forward portion of the body. These rough estimates are in qualitative agreement with the experimental results of References 7 and 9.https://authors.library.caltech.edu/records/thz0z-vee29Smog: a report to the people of the South Coast Air Basin. Part I. The EQL Strategy - A Summary (including Figures 1-14). Part II. The EQL Strategy - Legislative and Administrative Action Required
https://resolver.caltech.edu/CaltechAUTHORS:20160121-153353232
Authors: Lees, Lester; Borrelli, Peter; Easterling, Mahlon; Klein, Burton H.; Pauker, Guy; Poppe, Robert; List, E. John
Year: 2018https://authors.library.caltech.edu/records/qzcx3-9qt61Stability Theory for Cross Hatching. Part I. Linear Stability Theory
https://resolver.caltech.edu/CaltechAUTHORS:20190115-160036728
Authors: Lees, Lester; Kubota, Toshi; Ko, Denny R. S.
Year: 2019
A linear instability theory was developed which couples small perturbations in surface shape of a subliming surface and resulting perturbations in aerodynamic heat-transfer rates. Equations governing compressible turbulent boundary layers were linearized for small perturbations whose streamwise scale lengths are comparable with the undisturbed boundary layer thickness. For turbulent shear stress, the mixing-length approximation was employed, and the turbulent Prandtl number was assumed to be unity for turbulent heat flux. Heat conduction within the ablating solid was analyzed by linearizing the boundary condition for small amplitude. Sample computations were made for a teflon surface ablating under turbulent boundary layer at Mach 2. 6, and the results indicate that the small surface perturbations are unstable within certain regions in the wave number - wave angle space.https://authors.library.caltech.edu/records/1qg2w-fs610Stability Theory for Cross-Hatching. Part II. An Experiment on Turbulent Boundary Layer over a Wavy Wall
https://resolver.caltech.edu/CaltechAUTHORS:20190117-174447349
Authors: Lees, L.; Kubota, T.; Sigal, A.
Year: 2019
An experimental investigation of turbulent boundary layer flow over wavy surfaces was conducted at low speed. Two models with the ratio of the amplitude to the wave length a/λ = 0.03 and wave lengths λ = 6" and 12" were tested in an open-circuit wind tunnel. The free stream velocity was 15.4 m/sec, giving Reynolds number Re = 2.54 X 10^4 per inch. Boundary-layer thickness varied from δ = 1.5" to δ = 4.1" by means of boundary-layer trips of various height, in order to change the ratio λ/δ. The fol- lowing measurements were taken: wall pressure distribution, average velocity and turbulence level, wall stress distribution, static and total pressures, and shear stress distribution across the layer.
Wall pressure perturbation is much lower than predicted by uniform, inviscid theory and is slightly non-symmetric. Wall stress distribution has a peak with C_f/C_f_o = 1.2 upstream of the crest and a dip of C_f/C_f_o = 0.6 upstream of the trough.
The turbulence intensities and shear stress distributions near the wall show oscillatory modulation superimposed on the reference flat plate pro- files. The amplitude of the oscillations decays exponentially toward the edge of the layer, so that in the outer part of the layer the turbulence quantities are practically independent of the longitudinal position.https://authors.library.caltech.edu/records/mqamw-11s39