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i s NASA Contractor Report 159190 (NASA-CR-159190) UNSTEADY FLOW AND DYNAMIC NBO -14355 RESPONSE ANALYSES FOR HELICOPTER ROTOR
BLADES Final Progress Report, 2 Jan. 1971 -
30 Jun. 1979 (Wisconsin Univ. - Milwaukee.)
Unclas 30 p HC A03/MF A01 CSCL 02A 63/34 13965 UNSTEADY FLOW AND DYNAMIC RESPONSE ANALYSES FOR HELICOPTER ROTOR BLADES Final Progress Report Prepared by Theodore Bratanow for the National Aeronautics and Space Administration Under Grant No. NGR-50-007-001 r.
UNIVERSITY OF WISCONSIN-MILWAUKEE
Milwaukee, Wisconsin ^$192021^^^
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091^ rN Milwaukee, Wisconsin, November 1979 NASA Contractor Report 159190 UNSTEADY FLOW AND DYNAMIC RESPONSE ANALYSES FOR HELICOPTER ROTOR BLADES Final Progress Report Prepared by Theodore Bratanow for the National Aeronautics and Space Administration Under Grant No. NGR-50-007-001 UNIVERSITY OF WISCONSIN-MILWAUKEE Milwaukee, Wisconsin Milwaukee, Wisconsin, November 1979 UNSTEADY FLOW AND DYNAMIC RESPONSE ANALYSES FOR HELICOPTER ROTOF ;.ADES Final Progress Report Theodore Bratanow* University of Wisconsin-Milwaukee ABSTRACT This final report summarizes the research on the NASA-project for the period of January 2, 1971 to June 30, 1979. Wherever possible, an effort was made to provide a step-by-step chronological account and to note developments which are worth mentioning. The research was directed basically in two directions: starting with a helicopter rotor blade vibration analysis and then concentrat- ing on two and three-dimensional analyses of unsteady incompressible viscous flow past oscillating helicopter rotor blades. As can be seen, it was nec- essary to cover a wide range of aspects related to the research objectives.
Very often, it was necessary to piece together whatever and how little was known on the subject of the Reynolds number range.
A summary is presented also of the two international research collaborations which resulted from the NASA-project: the collaboration under the auspices of NATO between the University of Wisconsin-Milwaukee (UWM), University of Brussels, Belgium and the Aerodynamics Research Establishment (DFVLR) in Goettingen, W. Germany, and the collaboration under the auspices of the Na- tional Science Foundation between UWM and the University of Hamburg and the Ship Research Establishment in Hamburg (HSVA), W. Germany. Finally, a sum- mary is given of the benefits from the NASA-project to UWM, the College of Engineering and Applied Science, and the participants on the project. The numbers in the brackets refer to reports, publications, and graduate student theses related to the project.
*Professor TABLE OF CONTENTS Page ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . .
PARTICIPANTS IN THE INTERNATIONAL COOPERATIVE RESEARCH UNDER THE AUSPICES OF NATO . . . . . . . . . . . . . .
PARTICIPANTS IN THE COOPERATION UNTER THE . 5 AUSPICES OF NSF . . . . . . . . . . . . . . . . . . . . . .
SUMMARY OF THE RESEARCH . . . . . . . . . . . . . . 6 1. Introduction . . . . . . .
?. The Work with the Stream Function Vorticity Formulation.7 3. The Application of the Lighthill Procedure 4. Analysis of Three-dimensional Unsteady Flow Around Oscillating Wings . . . . . . . . . . . . . . .
INTERNATIONAL RESEARCH COLLABORATION RESULTING FROM NASA - PROJECT . . . . . . . . . . . . . 11 1. Introduction . . . . .
2. Summary of the Collaboration Under the . . . . . . . . . . . . . . . . .
Auspices of NATO The Early Period of the Collaboration with Goettingen 3.
4. The Measurement Program of 1975 . . . . . . . .
5. On the Collaboration with the University of Brussels . . .
. . . . . . . . 14 6. On the Assistance from Professor Gladwell 7. On the Collaboration Under the Auspices of NSF . . . . . .
BENEFITS FROM THE NASA - PROGRAM AT OUR UNIVERSITY . . . . . . . .16 1. Introduction .
Contribution of the NASA-Program to our College 2.
3. Benefits to the Participants on the Project . . . . . . .
PUBLICATIONS AND REPORTS GENERATED UNDER THE GRANT . . . . . . . .
LIST OF PAPERS AND REPORTS RELATED TO THE NATO PROJECT . . . . . .
Graduate Theses Under the NASA Grant . . . . . . . . . . . . . 22 iStudent Papers Presented at Meetings . . . . . . . . . . . . .
Figures 2-5 . . . . . . . . . . . . . . . . . . . . . . . . .
PARTICIPANTS IN THE INTERNATIONAL COOPERATIVE RESEARCH UNDER THE AUSPICES OF NATO I. AT THE UNIVERSITY OF W ISCONSIN IN MILWAUKEE, WISCONSIN, USA Principal Investigator: Dr. Theodore BRATANOW, Professor Engineering Mechanics, College of Engineering and Applied Science Mr. Thomas SPEHERT Research Specialist, Engineering Mechanics II. AT THE INSTITUTE OF AEROELASTICITY OF DFVLR IN GOETTINGEN, WEST GERMANY Principal Investigator: Dr. Hans FOERSCHING, Professor Director, Institute of Aeroelasticity Associate Principal Investigators: Dr. Wolfgang GEISSLER Head of the Theoretical Analysis Section Dr. Hermann TRIEBSTEIN Supervisor of Experimental Projects III. AT THE UNIVERSITY OF BRUXELLES-BRUXELLES, BELGIUM Principal Investigator: Dr. Charles HIRSCH, Professor Chairman, Department of Fluid Dynamics Dr. Guido DE GRANDE Research Associate THE PARTICIPANTS IN THE COOPERATION UNDER THE AUSPICES OF NSF In Hamburg, West Germany Dr. Otto Grim, Professor, Institute for Ship Research, University of Hambu r g, former director and presently member of the board of the Hamburgische Schiffbau - and Versuchsanstalt G.m.b.H., Hamburg Dr. Joachim Schwarz, Head, Ice Tank Research Facility of the Hamburgische Schiffbau - and Versuchsanstalt G.m.b.H., Hamburg Dipl.-Ing. Franz Haeusler, Scientist, Institute for Ship Research, University of Hamburg and the Hamburgische Schiffbau - and Versuchsanstalt G.m.b.H., Hamburg At the Universit y of Wisconsin - Milwaukee Dr. Theodore Bratanow, Professor, Department of Mechanics, College of Engineering and Applied Science Mr. Thomas Spehert, M.S., Research Associate SUMMARY OF THE RESEARCH 1. Introduction An effort was made to summarize the work on the project in a chronological order. A step-by-step discussion is given of the development of the analyses of the two- and three-dimensional flows which were not explained in our published work [1-22]. An explanation is given of the encountered computer difficulties. An effort was made also to assess realistically the results and the condi'.iins under which the project was carried out.
The Navier-Stokes equations were chosen as the mathematical model for the problem of unsteady incompressible viscous flow around oscillating rotor blade airfoils and wings. It appeared that these equations contained all the features needed to represent the actual conditions and that the prob- lem is amenable to such an approach. Above all, it appeared that this approach is the most fundamental one. As it happened a great deal could be learned in this way and some important conclusions drawn from the detailed analysis with these equations. Looking back now at the work on the project, there is very little doubt that the application of the Navier-Stokes equations was the way to go.
The vorticity-stream function formulation was applied initially for the solution of the problem at hand. The reasons for the decision to discon- tinue the work with this formulation are given. A new common method, suggested by Lighthill, was applied for both the two- and three-dimensional cases. It appears that this method represents efficiently the physics of the unsteady flow in a form suitable for numerical computation. See table and figure 1.
We set out to investigate the suitability J the formulation and to produce results for suitable Reynolds number flows. Those were days of difficulty and pressure. There was a strong determination of the project group to brave out every difficulty and to make progress and to succeed. A computer terminal was acquired for our laboratory and keeping a six-day work week became standard. Good results were obtained in spite of the limitations on advanced and comprehensive co m puter research work in a university environ- ment and the limitations of the UWM computer facility. We presented the results as they were obtained from the computer, letting the limitations of the applied formulation and the applied finite element technique be visible. We felt that our results were of interest to researchers and were appreciated by research engineers as samples of a first complete attempt on this complicated problem. There were over 100 requests from researchers all over the world of our many published papers. There have been already encouraging reviews of our papers.
Since UWM does not have the proper experimental facilities, we have been seeking cooperation. The two international research collaborations under the auspices of NATO and NSF were initiated and coordinated by this writer.
A very good working relationship was established. The results from care- fully prepared experiments contributed greatly toward our basic understanding of flow patterns and served as a guide in developing the analyses. See figures 2-5.
2. The Work with the Stream Function Vorticity Formulation In the first two years of the research on the flow around oscillating air- foils using the Navier-Stokes equations, we applied finite element grid- works in modelling the flow. The gridworks were composed of nonconformable third-order triangular finite elements with straight edges. These were of different sizes, usually small, closer to the airfoil, and larger, further away. Next to the stream function formulation and the velocity and pressure formulation, the stream function and vorticity formulation is one of the three formulations mostly used for incompressible viscous flow with inertia in conjunction with the finite-element method. One works here with two coupled equations of second-order in terms of the stream function and the vorticity. However, the stream function and vorticity formulation offers advantages only when applied to a two-dimensional analysis. The principal difficulty in using the stream function and vorticity formulation is that, in general, vorticity is unknown a priori along solid boundaries. Determi- ning the values for the vorticity along the airfoil boundary required de- tailed consideration since here the no-slip boundary condition alone is not sufficient.
'variational functionals equivalent to the governing differential equations in terms of stream function, vorticity and pressure were established. For the resulting differential equations in the form of Poisson's equations, in terms of stream function and pressure as the dependent variables, the exact forms of the variational functionals were available and were used all along.
No exact variational form exists for the representation of the vorticity transport equation due to the nonlinearity in the convective terms. Thus, an approximate variational functional was derived for the vorticity trans- port equation. By using the Minimum Functional Theorem and employing a Taylor series expansion of the velocity vector in terms of vorticity, an approximate minimization functional for the vorticity transport equation was obtained. The discretization process yielded two systems of algebraic equations corresponding respectively to the discretized form of the differen- tial equations for the stream function and pressure, and a system of first order ordinary differential equations in terms of the time derivative of the vorticity. The system of algebraic equations for the stream function and the system of algebraic equations for the pressure were solved at each time step of the numerical integration of the vorticity transport equation.
The system of first order ordinary differential equations corresponding to the vorticity transport equation was integrated with respect to time using a first order forward difference scheme.
The stability and convergence problems associated with the integration of the vorticity transport equation with respect to time, in particula. • , were continuously analyzed. Sufficient criteria was established for determining the range of applicability of the applied numerical method in terms of the flow parameters related to the computational procedure; the time step, size, and shape of the distribution of finite-elements in the gridwork in particular. The variation of the stream function over the nonconformable element was approximated by a complete cubic polynomial. Vorticity and pressure were considered to vary linearly over the triangular finite element. The method was applied first to flow around spheres and cylinders, and then to oscillating airfoils starting at arbitrary mean angles of attack. The accuracy of the boundary conditions applied for the example with the NACA 0012 airfoil and their incorporation into the finite element formulation was determined by numerical experimentation. We explained that with the nonconformable finite element, we obtained discontinuous repre- sentation of boundary values, thus causing deviations from the no-slip condition between the nodal boundary points where the no-slip condition was specified.
Close attention was paid to minute details related to the established var- iational functionals for stream function, vorticity, and pressure and how their discretized form affected the overall accuracy of the computational procedure. The adverse effect on accuracy due to the nonuniformity in size and shape of the applied straight edge finite elements was recognized very early in our work and continued to present difficulty with the vorticity stream function formulation. The problem conditions, factors, and para- meters affecting the accuracy of our finite element solution were exten- sively presented and discussed in all of our papers. 'he question of the effect of the accuracy of the solution when defining an cuter boundary of the flow around an oscillating airfoil was given attention. When we suspected inaccuracy, we changed the range of the outer boundary. With the boundary defined, we did not observe any significant inaccuracy due to the outer flow boundary. As a guide in selecting the outer boundary, we used magnified frames of the film by Professor Hazen on "Boundary Layer Control" and suitable photographs of wind tunnel experiments.
Finally, a Gordian Knot, a problem of most difficult solution in dynamics applications using the finite element method, is the discretization with respect to time. We thought that the discretization of the time variable by the finite element method would introduce disadvantages from a computa- tional point of view. And at the time there was no proven advantage report- ed in the literature. This statement does not, however, mean that there are no advantages in time discretization, but rather, that there has been very little (even up to now) research done in this direction and as such the advantages have not become clear. One of the generally known advantages of discre ,^ization in time using the finite element method is that of better convergence and stability, or in other words, the possibility of using larger time step in the numerical integration. This advantage leads to less computational time for the solution of the problem.
3. The Aaalication of the Liahthill Procedure In light of the already discovered facts and from their correct interpreta- tion, there were indications where revisions in the formulation and in the numerical procedure should be made. From the arbitrariness and the uncor- related pressure distributions of some of the results, in particular, there were unmistakable clues that somethirg about the oscillating airfoil was either not properly done or was not represented at all. The decision to discontinue using the vorticity-stream function formulation was based, also, on the realization that the up-to-date development of the techniques and procedures involved with the application of this formulation were still as well as the limitations of the straight edge finite elements, inadequate, and the inadequacy of the available computer and software. Finally, the amount of the computer storage needed reached the maximum analysis for higher Reynolds number flows. And then, the computer programs were spec- ially segmented in order to meet capabilities of the 1106 Univac computer.
The two most important and obvious components of the analysis to improve on were the formulation and the applied finite element. All along we were alert on introducing improvements and refinements in the package of computer programs because around the end of the year 1974, our university introduced a computer with inferior overall capability than we had until then. Name- ly, the state-wide Univac 1110 computer system used was replaced by our own Univac 1108 computer installed on our campus. This change then worked against our aspirations to increase the overall size of solution procedure in order to increase accuracy of our results. This simple fact continued to plague us almost until the end of November 1975.
The vorticity transport equations were cast in a form convenient for compu- tation. The computation is considered unsteady in the sense of being suit- able for time-stepped solutions. A statement for these equations was written using the method of weighted residuals and applying the Galerkin criterion. From the discretized form of the equations, finite-element equa- tions were assembled and summed over all elements forming thus the global system of equation for the complete flow region. The discretization in finite-element form of the vorticity transport equations resulted in a system of differential equations with respect to time. These equations can be solved with respect to the time variable using a finite difference technique. Finite-elements in the fluid region contain vorticity, since vorticity will be found only in that portion of the fluid region which is discretized by finite-elements.
An integral representation of the induced velocity at finite-element nodes due to the vorticity distribution was applied on the basis of the Biot- Savart law. The numerical procedure developed by Hess and Smith and then refined by Argyris and Scharpf was used in computing vortex sheets over by Argyris and Scharpf the curved wing surface. The refinement int r oduced involved curvilinear elements, in place of the plane elements used by Hess and Smith. A Hermitian interpolation model was used to approximate the geometry of curvilinear elements between nodes defining the elements. A Lagrangian interpolation model was used to describe vortex sheet intensity over finite-elements. Two types of finite-elements were applied in repre- senting the flow region under investigation: isoparametric triangular and isoparametric quadrilateral finite-elements. Surrounding the curved wing surface are quadrilateral finite-elements, with the remainder of the fluid region divided into triangular finite-elements of varying sizes, becoming smaller and smaller near the wing surface. Quadratic shape-functions were utilized for both isoparametric triangular and isoparametric quadrilateral finite-elements.
ANALYSIS OF THREE - DIMENSIONAL UNSTEADY FLOW AROUND OSCILLATING WINGS Mathematical Background 3 w v) w = (w • v)u — vv 2 W (1) 2i + (u • V x u = w (2) v • u 0 (3) 0 2 p - —pV [v (U U)] (4) Numerical Integration of the Vorticity Transport Equations aw. aw.
m = dV + 2 wiu j dV
wi at axe V V j _ v awi )l 2 1 a2ui 2 w i w j 2 dV (5) 2 \ax./ dV - 3 ax f v v j aui 1 a2ui u i = u i j ew k + •• (6) +
awl ° w j + 2 awl ew . .awk
t o ^ o ^ o wj (x.y,z) = A i (x.y,z)w^ (7) dW INTERW Y ONAL RESEARCH COLLABORATIONS RESULTING FROM THE NASA-PROJECT Introduction 1.
The NASA-research program truly combines several specialized disciplines for a common purpose. The research approaches had to involve team activities.
have been impor- The collaboration aspect of the program was considered t o tant for its success. It was founded on the conviction that more significant contributionF can re made when working together. The collaborations are Judged to have L';E^2n of special significance because they coupled university research at UWM, Brussels, and Hamburg, and applied research resources of Goettingen and Hamburg. They gave an added dimension to our capability and they gave us an opportunity to participate in a research on a larger scale.
The specialized resources and capabilitietin Goettingen, Brussels, and Hamburg, in a way, became available to us. The established collaboration offered an exciting opportunity for a contribution on a wide front in the emerging field of Unsteady Aerodynamics.
Special comments can be made on the relation between the participants in the collaborations. lhey rested on a solid foundation of confidence and deter- mination to contribute to the development of basic science. The p rojects did more than just stimulate collaboration between the scientists. The up-to- date record of the collaborations show that the research teams brought about do exchange of ideas, experience, and capability as well as research contri- butions which are truly more significant than the total of individual nation- ally supported projects.
The collaborators adopted a long-term far-reaching comprehensive approach to the goals of the research. Substantial national support was obtained for the basic costs. Existing experimental facilities were expanded. New equip- ment was procured. Elaborate models were built. A new and ,jriique high- pressu r e wind-tunnel in Goettingen is nearing completion.
The fol l owing, then, is a summary of the collaboration activities, of the work already accomplished, and of the work in progress. A complete list [23-45] is included of the papers and reports related to the collaborations under the auspices of NATO and the National Science Foundation in Washiritri, D.C. Several of the papers listed presented results of far-reaching impor- tance from both fundamental and applied aspects.
2. Summary of the Collaboration under the Auspices of NATO The objectives of the conducted research program can be summarized as follows: For the example of osciilatory motion, during operational conditions, of helicopter rotor blades, through a coordinated systematic theoretical compu- tational end Experimental research, a method of analysis will be developed for: forces and unsteady pressure distributions on the oscillating wing surfaces; nature and details of the unsteady viscous flow around blade tips; the manner in which the oscillatory motion affects the turbulence structure of the unsteady flow around the oscillating wing. The example of the os- cillating helicopter rotor blade was chosen because it represents the most interesting and most complete example of the three-dimensional unsteady aerodynamics for which fundamental knowledge is needed.
The distribution of work-load continued along the following lines: at the University of Wisconsin-Milwaukee, theoretical and computational analyses of unsteady viscous flow and unsteady pressure distributions around oscillating two-dimensional airfoils and blades; at DFVLR in Goettingen, both experimen- tally and theoretically, research with prime emphasis on unsteady pressure m!asuremen's on two-dimensional airfoils and blades 'n their subsonic and high Reynolds number wind-tunnels; at the University of Brussels, determini,ig effects of the oscillatory wing motion on the flow separation and turbulence structure of the unsteady flow around oscillating two-dimensional airfoils and blades; both experimentally and theoretically.
3. The Early Period of the Collaboration with Goettingen For a :oordinate^ and concentrated attack on the overall problem of the oscilldting blade, this writer sought and succeeded in laying out the ground work for a collaboration with the Institute of Aeroelasticity of DFVLR - Goettingen. The first contr::t in September of 1973 was made pos- sible with the help of Dr. Wolfgang Geissler. He made the introduction to the Director of the Institute. Professor Hans Foersching, who came out to be an alumnus of mine. It happened that they were seeking to establish contacts in :ne U.S.A. too. They were delighted that in this context they were to establish collaboration with NASA - Langley. Upon return to the U.S.. a report was submitted to Mr. John F. Ward, then of NASA - Langley.
Initial details of a mechanism for starting a collaboration were discussed.
On my second visit to Goettingen in January of 1974, I presented an outline of v -ofessor a suitable testing program related to my work. Foersching agreed to carry `t out. It was intended on their part to be a goodwill gesture toward NASA - Langley. In June of 1974, Ur. Geissler and I visited Langley and then he came to UWM. We became familiar with each other's work.
Further details of the collaboration were worked out, and the prospect for experimental correlation of results came closer to reality.
In April of 1975, Goet.tingen carried out. at the expense of 100,000 German Marks, a very interesting experimental measurement program on a full-scale helicopter blade tip (see Fig. 2). The blade is still referred to as the .-P "Bratanow Wing". Unsteady three-dimensional pressure distributions w measured and documented (see belo-N). In June of 1975, Professor Foersching visited Milwaukee and Langley. Dr. Geissler spent three months in the summer of 1975 at UWM. The UWM - Graduate School helped in the undertaking and supported his family during their visit in Milwaukee. It was i very good occasion for a meaningful cooperation and exchange of ideas.
4.
The Measurement Program of 1975 [411 Measurements were made of pressure distributions on the harmonically Y oscillating rotor blade wing in low subsonic speed. The measurements were carried out in the 3 X 3 m-subsonic wind-tunnel of the DFVLR in Goettingen.
Pressures were measured at five sections of the wing in a way that the three-dimensionality of the pressure distribution could be well observed.
The flow speed was 45 m/s. The oscillation frequencies were 2, 4, 6 Hz; with reduced frequencies o*-,rfl/V=0.07, 0.14, and 0.21. The oscillation amplitutl es ranc,2d from B = 1° to 3°, and the angles of attack were a = 0', J% 6% 9', and 12°. Comparisons with theoretical and experimental results were made. The calculated predictions were found to agree well with the measured data. At the wing tip, however, the agreement was not uniform. A description of the test-facility used is also presented in [41].
5. On the Collaboration with the University of Brussels, Belgium Professor Charles Hirsch, Head of the Department of Fluid Dynamics of the University of Brussels, is the other principle investigator in the collab- oration under the auspices of NATO. He has a strong theoretical and exper- imental background in Fluid Dynamics and Aerodynamics.
The period of July, 1975 to April 1, 1976 in several ways was a decisive period in the course of the project. Changes in the conduct of the research program were made and proved to be very beneficial for the overall outcome of the project. Looking back to the experience, I realize now that in that period I actually put my determination to successfully finish the project above everything else. When confronted with the enormous complexity of the computational undertaking with the vorticity-stream function formulation for the two-dimensional analysis, I forgot my personal pride and secured the cooperation of Professor G.M.L. Gladwell of the University of Waterloo, Ontario, Canada and Professor Hirsch from the University of Brussels, Belgium. It was thus possible to develop a new, unified, and from a phys- ical point of view, more complete, yet simp.^r, method of attack for both the two- and three-dimensional analysis of unsteady flow around oscillating wings.
Professor Hirsch visited UWM in September of 1975 and then for about one week in March of 1976, to familiarize himself with our work. He not only assisted in our work but also expressed a desire to contribute to our further, down-stream, efforts to analyze the effects of the oscillating wing on the transition and turbulence patterns of the unsteady flow. A comprehensive contribution in this area would have involved efforts beyond the ones expected in this research or)gram.
After reviewing the iteration procedure, prepared by my research associate at UWM Mr. Thomas Spehert, Professor Hirsch was of the opinion that the procedure developed by Thomas is sound and that it ultimately will lead to a significant reduction in computational difficulties. Professor Hirsch inserted several fea`-,res in the iteration procedure to increase the con- vergence. A proposa l for funding of the mechanism for the cooperation be- tween Brussels, DFViR and UWM was submitted un September 15, 1976 to the NATO Research Office in Brussels, Belgium.
On the Assistance from Professor Gladwell 6.
When I felt a need for an effective consultation regarding our numerical computational difficulties, Professor G.M.L. Gladwell, a mathematician and friend, agreed to assist. Professor Gladwell is from the University of Southampton, England, and is now at the University of Waterloo, Ontario.
He has an outstanding reputation as an expert in numerical analysis. He was very eager to get involved with the project and help me out. Such consultation is actually something which I should have secured much sooner.
In the second half of August, 1975, I sent Mr. Thomas Spehert to see Professor Gladwell. He agreed that Thomas was on the right track; the pro- cedure was to be a common procedure for both the two- and three-dimensional analyses. Professor Gladwell also gave a good set of recommendations and guidelines. Thomas accepted the challenge and engaged in a further detail- ed research. At the end of October, 1975, Professor Gladwell came here to discuss the progress Thomas had made and there was then a useful exchange and coordination of ideas. At the end of November, 1975, Thomas went to see Professor Gladwell again. Professor Gladwell has helped us, also, in adapting the use of curvilinear (isoparametric) finite elements for improved representation of the wing boundary. In the first week of March, 1976, Thomas went again to see Professor Gladwell and by then the iteration pro- cedure of the oscillating wing analysis was finalized.
On the Collaboration under the Aus p ices of N.S.F.
7.
The research collaboration under the auspices of N.S.F. between UWM, the University of Hamburg, and HSVA of Hamburg, West Germany represents the other major benefit of the NASA - research project. The objectives of the conducted research program will now be summarized.
We have been working on a more consistent and generally applicable drag resistance analysis for ships. The impetus for this work has its origin in the problem of drag reSistance to motion in a dense mixture of fluid and solid particles around an actual ship in a shipping channel clogged with broken (mush) ice. The example of the conditions in the St. Marys River in the peninsula of Upper Michigan during the winter months offers a unique opportunity for an application o; the developed concept.
The specific objective of the research program is to carry out systematic investiCation for the development of a theoretical method for determining the portion of the total encountered resistance by an icebreaking ship moving in unbroken plate ice which is due only to the broken ice particles around the ship hull. In particular, efforts were made to develop mathe- matical models and computational procedures toward the solution with the three-dimensional equations for viscous flow motion. Efforts have been directed toward the analysis of viscous flow characteristics and the drag resistance to continuous steady motion of a solid body of arbitrary geometry in a dense mixture of fluid and solid particles.
4 -.
For the proper modelling of the more difficult problem of determining the flow motion at lower Reynolds numbers, we use the steady state nonlinear Navier-Stokes equations. Such a treatment is an interesting approach for constructing the numerical solution in the three-dimensional case. The equations allow for a systematic investigation. An analysis with the Navier-Stokes equations can be formulated with any slip condition at the hull surface; with either no-slip, intermediate slip, or variable slip.
Iteration can be carried out either up to the prescribed percentage of the no-slip condition or with a variable function. It appears that under low Reynolds number conditions the internal viscosity of the mush ice is large enough to render a conventional boundary-layer analysis invalid. Finally, such an analysis is better able to represent the trailing vorticity in the wake than any boundary-layer approach would. See figures 3-5.
The analytical method has the potential for direct application to more efficient design of ship hulls and aircraft fuselages and for reducing the amount of presently required testing in model tanks and wind tunnels. Of special consideration affecting the research program is the demonstration test case of ship motion in a channel clogged with broken ice blocks. It is expected that the research will result in answers to questions which are of special significance to this fundamental phenomenon.
BENEFITS FROM THE NASA-PROGRAM AT OUR UNIVERSITY Introduction 1.
The University of Wisconsin-Milwaukee (UWM) appreciates the benefits which -research goals and to UWM from the NASA have accrued both to the NASA sponsored research program. The period of duration of the NASA program here has coincided with the period of significant growth of UWM. Recent years have seen a rapid increase in the number of under-graduate and graduate students as well as faculty members on the Milwaukee campus. This growth in enrollment has coincided with corresponding growth in research activities.
The NASA- program has provided a strong technological orientation of these activities.
The Graduate School of UWM, for instance, has been enthusiastically encour- aging this research activity of ours. Since the commencement of the project, it has been effectively supporting us in several ways; by partly paying salaries of people working on the project and by paying the salary of visiting scholars like Dr. Kiciman and Dr. Geissler to contribute to our program; by partially paying the expenses connected with presenting papers at internation- al meetings overseas and particularly by supporting us with computer funds.
2. Contributions of the NASA-Program to our College The College of Engineering and Applied Science is relativeiy new on the UWM campus since about 15 years now. It is an ECPD accredited school and it has a notable responsibility and opportunity to produce highly competent engi- neers. The college has provided education on Master's and Doctoral levels.
The NASA-project was primarily instrumental and helpful in the process of establishing the Doctoral degree program in the college. Because of its unique nature, this research project has helped strengthen the overall re- search capability of the college. Above all, the project has helped enhance the national and international reputation of our college when one considers that there have been about 100 requests for our papers from the U.S. and all over the world.
There has been a sizeable aeronautically oriented industry and a well known commercial aircraft activity in the state of Wisconsin. They have provided a career destination for our graduates. Finally, this project has helped our department to gain a valuable experience in a vital branch of transpor- tation.
3. Benefits to the Participants on the Project -sponsored research program has been very beneficial to the partici- The NASA pating students, faculty members, and visiting scientists. It has contributed toward their professional development. They have acquired an excellent ex- perience with aerodynamics, numerical computational methods, applied mathematical analysis, fluid dynamics, and hydrodynamics [46-52].
The following participated on the project: Students; 1. Gary Driesen, now with Westinghouse Electric Company 2. Michael Kobiske, Eaton Corporation 3. Thomas Spehert, Harley-Davidson 4. Joseph Eichers, Aqua-Chem Corporation Gerald Baker, McDonnell-Douglas Corp.
5.
Kenneth Rademacher, Wisconsin Electric Power Co.
6.
7. Robert Farchione, Harley-Davidson 8. Dean Kaja, professional engineer 9. Frederic Chudy, United Aircraft Corporation 10. Gary Exner, professional engineer Huseyin Aksu, professional engineer 11.
Perry Kirsop, presently graduate student at UWM 12.
In addition, a good number of undergraduate students participated as part time assistants and typists, and benefited from the project in their pursuits of higher education.
The grant has also contributed toward the professional development of the participating visiting scientists: 1. Dr. M.O. Kiciman, now president, University of Ankara, Ankara, Turkey 2. Dr. H. Foersching, Aerodynamics Research Establishment, Goettingen, W. Germany 3. Dr. W. Geissler, Aerodynamics Establishment, Goettingen, W. Germany Dr. C. Hirsch, University of Brussels, Brussels, Belgium 4.
5. Dr. G.M.L. Gladwell, University of Waterloo, Waterloo, Canada Dr. Kiciman contributed for three months in the summer of 1973 as visiting professor on the project at no expense to the project and was paid by the Graduate School of UWM. Dr. Kiciman helped in developing the optimization technique applied in our three-dimensional flow analysis. Dr. Akin Ecer is a practicing scientist in Cincinnati, Ohio.
Finally, the NASA-project contributed greatly toward the professional devel- opment of the Principal Investigator. In the past he has been repeatedly invited to present papers at international conferences and to present lectures at universities and aircraft companies on the work related to this project.
w, PUBLICATIONS AND REPORTS GENERATED UNDER THE GRANT 1. Bratanow, T., Ecer, A. and Kobiske, M , "Finite Element Analysis of Unsteady Incompressible Flow Around an Oscillating Obstacle of Arbitrary Shape", AIAA Journal, Vol. 11, No. 11, Nov. 1973, pp.
1471-1477; presented also as paper 73-91 at the AIAA - 11th Annual Aerospace Sciences Meeting in Washington, D.C., Jan. 10-12, 1973.
2. Bratanow, T. and Ecer, A., "On the Application of the Finite Element Method in Unsteady Aerodynamics", AIAA Journal, Vol. 12, No. 4, April 1974, pp. 503-510.
3. Bratanow, T. and Ecer, A., "Analysis of Three-dimensional Unsteady Viscous Flow Around Oscillating Wings", AIAA Journal, Vol. 12, No.
11, Nov. 1974, pp. 1577-1584; presentee also as paper 74-184 at the AIAA - 12th Annual Aerospace Sciences Meeting, Washington, D.C., Jan.
30 - Feb. 1, 1974.
4. Bratanow, T. and Ecer, A., "Sensitivity of Rotor Blade Vibration Characteristics to Torsional Oscillations", AIAA Journal of Aircraft, Vol. 11, No. 7, July 1974, pp. 375-381; presented also as paper 73-404 at the AIAA/ASME/SAE - 14th Structures, Structural Dynamics, and Materials Conference, Williamsburg, Va., March 20-22, 1973.
5. Bratanow, T., Ecer, A. and Eichers, J., "Analysis of Three-dimen- sional Potential Flow Around a Ship Hull", AIAA Hydronautics Journal, Vol. 9, No. 2, April 1975, pp. 64-68.
Bratanow, T. and Ecer, A., "Suitability of the Finite Element Method for Analysis of Unsteady Flow Around Oscillating Airfoils" Numerical Methods in Fluid Dynamics - Proc. Int. Conference, Univ.
of Southampton, England, Sept. 26-28, 1973, Pentech Press, London, 1974, pp. 186-219.
Bratanow, T. and Ecer, A., "Analysis of Moving Body Problems in 7.
Aerodynamics". Fin i te Element Methods in Flow Problems, a collection of papers presented at the Int. Symp., Univ. of Wales, Swansea, England, Jan. 8-12, 1974, edited by J.T. Oden, O.C. Zienkiewicz, R.H.
Gallagher, and C. Taylor, UAH Press, Huntsville, Ala., pp. 225-241.
8. Bratanow, T., Ecer, A., Aksu, H. and Spehert, T., "Nonlinearities in Analyses of Unsteady Flow Around Oscillating Wings", Computational Methods in Nonlinear Mechanics, Proc. Int. Conf., Univ. of Texas, Austin, Texas, Sept. 23-25, 1974, edited by J.T. Oden, pp. 925-934.
9. Bratanow, T. and Ecer, A., "Computational Considerations in Applica- tions of the Finite Element Method for Analysis of Unsteady Flow Around Airfoils", Proc. AIAA-Computational Fluid Dynamics Conf., Palm Springs, Calif., July 19-20, 1973, pp. 109-122.
10. Bratanow, T. and Ecer, A., "Finite Element Analyses and Computer Graphic Visualization of Flow Around Pitching and Plunging Airfoils", NASA CR-2249, Sept. 1973.
Bratanow, T., Ecer, A. and Kobiske, M., "Numerical Calculations of 11.
Velocity and Pressure Distribution Around Oscillating Airfoils", NASA CR-2368, Feb. 1974.
12. Bratanow, T. and Ecer, A., "Sensitivity Analysis of Torsional Vibration Characteristics of Helicopter Rotor Blades", Part 1, Structural Dynamics Analysis, NASA CR-2379, March 1974.
13. Bratanow, T. and Ecer, A., "Sensitivity Analysis of Torsional Vibration Characteristics of Helicopter Rotor Blades", Part 11, Aerodynamics and Sensitivity Analysis, NASA CR-2380, March 1974.
14. Bratanow, T., Aksu, H. and Spehert, T., "A Rigorous Solution of the Navier-Stokes Equations f -r Unsteady Viscous Flow at High Reynolds Numbers Around Oscillating Airfoils", Paper No. 75-863, Proceedings, AIAA - 8th Fluid and Plasmadynamics Conference, Hartford, Conn., June 16-18, '1975.
15. Bratanow, T., Aksu, H., Spehert, T. and Exner, G., "On the Accuracy of Solutions of the Navier-Stokes Equations for Unsteady Viscous Flow at High Reynolds Numbers", Proceedings, Int. Conf, on Mathematical Models for Environmental Problems, Univ. of Southampton, England, Sept. 8-12, 1975, Pentech Press, London, pp.
423-436.
16. Bratanow, T., Ecer, A. and Driesen, G., "Effects of Aerodynamic Damping and Mass on Vibration Characteristics of Helicopter Rotor Blades at High Forward Speeds", presented at the Symp. on Propulsion System Structural Integration and Engine Integrity, held at the Naval Postgraduate School, Monterey, Calif., Sept, 3-6, 1974.
17. Bratanow, T. and Geissler, W., "Loesung der instationaeren, zweidimensionalen incompressiblen Navier-Stokes-Gleichungen mit Hilfe des Finite-Element-Verfahrens", Interner Bericht IB 253-75 J 07, Deutsche Forschungs-und Versuchsanstalt fuer Luft-und Raumfahrt, Goettingen, W. Germany, Sept. 29, 1975.
Bratanow, T. and Spehert, T., "Recent Findings on the Inclusion of 18.
Vorticity in the Numerical Analysis of Unsteady High Reynolds Number Flows", Int. Conference on Applied Numerical Modelling, Univ. of Southampton, Southampton, England, July 11-15, 1977, Pentech Press, London, 1978, pp. 621-630.
19. Bratanow, T. and Spehert, T., "Computational Flow Development for Unsteady Viscous Flows", Part 1 - Foundation of the Numerical Method, NASA CR-2995, May 1978.
20. Bratanow, T., Spehert, T. and Brebbia, C.A., "Three-dimensional Analysis of Flows Around Ship Hulls Using Boundary Elements", Int. Conf, on "Recent Advances in Boundary Element Methods" Univ. of Southampton, Southampton, England, July 5-7, 1978, Pentech Press, London, England, 1978, pp. 105-122.
21.
Bratanow, T. and Spehert, T., "Numerical Modelling of Unsteady Viscous Flow Past a Circular Cylinder" Second Int. Conf. on Applied Numerical Modelling, Univ. of Madrid, Madrid, Spain, Sept. 11-15, 1978, pp. 1V-7.1-1.10.
22. Bratanow, T., "The Navier-Stokes Equations, Theory and Numerical Analysis", review of the book Navier-Stokes Equations by Roger Teman, North-Holland Publishing Company, Amsterdam, 1977, I.P.C. Science and published in Applied Mathematical Modellin g , Technology Press Lim., Guildford, Surrey, England, Vol. 3, April 1979, p. 159.
LIST OF PAPERS AND REPORTS RELATED TO 'THE NATO PROJECT At the University of Brussels - Belgium De Grande, G., Haverbeke, A., and Hirsch, Ch., "Digital Processing of 23.
Unsteady Periodic Signals with Application to the Turbulence Structure around Oscillating Airfoils", to be presented at the I.C.I.A.S.F. - con- ference, Monterey, (U.S.A.), September, 1979.
24. De Grande, G., "The Turbulence Structure in the Decay Region of a Three- Dimensional Turbulent Boundary Layer", GAMM workshop, Brussels, June, 1978.
25. De Grande, G., and Hirsch, Ch., "Three-Dimensional Incompressible Turbu- lent Boundary Layers", Report VUB-STR-8, October, 1978.
26. Hirsch, C. and Warzee, G., "An Integrated Quasi-3D Finite Element Calcula- tion Program for Turbomachinery Flows", Paper No. 78-GT-56, ASME Publication.
27. Hirsch, C. with Kool, P. and DeRuyck, J., "The Three-Dimensional Flow and Blade Wake in an Axial Plane Downstream of an Axial Compressor Rotor", Paper No. 78-GT-66, ASME Publication.
28. Hirsch, C. with Kool, P. and DeRuyck, J., "An Axial Compressor End-Wall Boundary Layer Calculation Method", Paper No. 78-GT-81, ASME Publication.
29. De Grande, G. and Kool, P., "An Improved Experimental Method to Determine the Complete Reynolds Stress Tensor with a Single Rotating Hot Wire", to be published.
At DFVLR - Goettingen - West Germany 30. Geissler, W. and Schmid, H., "Comparison Calculations between the DFVLR- Panel Method and the MBB-Equivalent Slope Method", A Method for Calcula- tion of Unsteady Airloads on Lift Surfaces with Rudder. (IB-253-78 J 01) 31. Geissler, W., "Nonlinear Unsteady Potential Flow Calculations for Three- Dimensional Oscillating Wings", AIAA Journal, Vol. 16, No. 11, November 1978, pp. 1168-1174.
32. Geissler, W., "Calculation of Unsteady Airloads on Oscillating Three- Dimensional Wings and Bodies", AGARD, Paper Reprinted from Conference Proceedings No. 227 Unsteady Aerodynamics.
33. Geissler, W., "Das Interferenzproblem Des Schwingenden Rumpfes In Bodennahe", on the occasion of the 70th birthday of Professor Hermann Schlichting.
34. Geissler, W., "Der harmonisch schwingende Rumpf in Unterschallstroemung - Einfluss der Kompressibilitaet - Forschungsbericht, DFVLR-FB 78-24, November 1978.
Geissler, W., "Berechnung der Druckverteilung an harmonisch oszilliere-iden 35.
dicken Ruempfen in inkompressibler Stroemung", Forschungsbericht, DLR-FB 76-48.
Foersching, H., Hochdruck-Windkanal fuer aerodynamische and aeroelastische 36.
Untersuchungen - insbesondere von Hochbaukonstrucktionen - bei Reynolds- zahlen bis 1,5 10 in inkompressibler Stroemung", DFVLR-AVA-Bericht 253 - 76 J O1 (1976).
37. Geissler, W., "Calculation of Unsteady Airloads on Oscillating Three- Dimensional Wings and Bodies", Paper No. 5, AGARD Fluid Dynamics Panel Symposium on Unsteady Aerodynamics, 26. - 28., September 1977, Ottawa, Canada.
38. Geissler, W., "Berechnung der Druckverteilung an oszillierenden drei- dimensionalen Tragflaechen mit endlicher Dicke in inkompressibler Stroemung", DFVLR-AVA-Bericht 253 - 76 J 05 (1976).
39. Triebstein, H., "Instationaere Druckverteilungsmessungen an angestellten Rotorblattspitzen in inkompressibler Stroemung", DLR-EB 76-42.
40. Triebstein, H. and Wagener, J., "Measurements of Pressure Distributions During Runs of the E 103 in Free Directions and in Tunnels", Aerodynamics of Fast Trains 7, 8 July, 1978 in Goettingen, West Germany.
41. Triebstein, H., "Unsteady Pressure Measurements on Rotor Blade Tips with Incidence in Incompressible Flow", AIAA Journal, Vol. 17, No. 7, July 1979.
42. Triebstein, H., "Unsteady Pressure Measurements on Wing-Storage Combination in Incompressible Flow", to be published in the Zeitschrift fuer Flugwissen- schaft.
43. Triebstein, H., "Transient Pressure Measurements at the Top of the Engine 103 During the Passage Through the Heitersberg Tunnel", Third Int. Symp.
on Aerodynamics and Ventilation of Vehicle Tunnels, 19-21 March, 1979, Sheffield University, Sheffield, England.
44. Kienappel, K., "Unsteady Aerodynamic Pressure Measurements en Rotating Lifting Systems", Archives of Mechanics, 1978.
45. Send, W., "Zur Theorie des Rotorblattes in Incompressible Stroemung", Internal Report 253 - J(10) (1978).
Graduate Theses Under This NASA-6rant 46. Kobiske, M., An Application of the Finite-Element Method Around Pitching and Plunging Rotor Blade Airfoils, UWM, December 1972, M.S. Thesis.
47. Driesen, Gary, Evaluation of Unsteady Aerodynamic Effects and Effects of Variations of Elastic Axis, Center of Gravity and Aerodynamic Center on Dynamic Response Characteristics of Rotor Blades, UWM, September 1972, M.S. Thesis.
48. Baker, N.G., Evaluation of the Applicability of the Lifting Line and Lifting Surface Theories in Dynamic Response Analysis of Rotor Blades, UWM (incomplete), M.S. Thesis.
49. Aksu, H., Nonlinear Mathematical Analysis of the Accuracy of the Navier- Stokes Equations in Applications for Unsteady Viscous Incompressible and Compressible Flow Around Oscillating Airfoils and Wings, Ph.D. Thesis (incomplete).
50. Spehert, Th., On the Analysis of Three-Dimensional Incompressible Viscous Flow Around Oscillating Wings, M.S. Thesis, completed in April 1979.
51. Kirsop, Perry, A Procedure for Calculating Streamlines Around Three- Dimensional Bodies, M.S. Thesis, to be completed in February 1980.
Student Papers Presented at Meetings 52. Kaja, Dean, Application of Computer Graphics Methods in Visualization of Flow about an Airtoil, 1971 Great Lakes Student Conference, Wright- Patterson AFB, Dayton, Ohio, May 7-8, 1971. (Organized by AIAA).
53. Spehert, Thomas and Eichers, Joseph, Application of the Method of Singularities to Potential Flow, 1974 AIAA Midwest Regional Student Conference, Champaign, Illinois, April 27, 1974.
There were two more graduate students supported from this project who did not complete their work: Dean Kaja, and Gary Exner.
1,2 Fig.l. Three-dimensional finite element gridwork.
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w v c u IA v' L L ^ z O+ a^ U .1 H O (U E G cd .^ N r+ ctl F+ a CL) F c7 a^ 3 a 7 ^ In w O +j O G b O ^4j O a .r ^ O O CD U 4,a u O U G O •r-, +j N O a^ a N v ^.•' N W •r 44 4U O N U G Lei O ••+ • r+ b v N .4 Ln N ^ C U N •4 .r O W Ln v L rn LA- a 1. Report No. Acceaaion No.
2. Government 3, Recipient's Catalo • No.
NASA CR-159190 4. Title and Subtitle 5. Report Date November 1979 UNSTEADY FLOW AND DYNAMIC RESPONSE ANALYSES FOR 6. Performing Organization Code HELICOPTER ROTOR BLADES 7. Authors) 8, Performing Organization Report No Theodore Bratanow 10 Work Unit No, 9. Performing Organization Name and Address University of Wisconsin-Milwaukee 11.
Contract or Grant No Milwaukee, Wisconsin 53201 NGR-50-007-001 Type of Report and Period Covered 12. Sponsoring Agency Name and Address Contractor Report National Aeronautics and Space Administration 14 Sponsoring Agency Code Washington, D.C. 20546 15. Supplementary Notes Warren H. Young, Jr.
Langley Technical Monitor: Progress Report 16, Abstract This final report summarizes the research on the NASA-project for the period of Wherever possible, an effort was made to provide January 2, 1971 to June 30, 1979.
a step-by-step chronological account and to note developments which are worth men- The research was directed basically in two directions: starting with a tioning.
helicopter rotor blade vibration analysis and then concentrating on two and three- dimensional analyses of unsteady incompressible viscous flow past oscillating helicopter rotor blades. As can be seen, it was necessary to cover a wide range of Very often, it was necessary to piece aspects related to the research objectives.
together whatever and how little was known on the subject of the Reynolds number research collaborations range. A summary is presented also of the two international the collaboration under the auspices of NATO which resulted from the NASA-project: Belg`uirl, (UWM), University .f Brussels, between the University of Wisconsin-Milwaukee anj the and the Aerodynamics Research Establishment (DFVLR) in Goettengen, W. Germany, Science Foundation between UWM and collaboration under the auspi:es of the National the University of Hamburg and the Ship Research Establishment in Hamburg (HSVA), W. Germany. Finally, a summary is given of the benefits from the NASA-project to UWM, the College of Engineering and Applied science, and the participants on the project.
The numbers in the brackets refer to reports, publications, aild graduate student theses related to the project.
17.
Key Wordt (Suggested by Author(s)) 18 D-str,bution Statement FINITE-ELEMENT ANALYSIS UNCLASSIFIED - UNLIMITED NAVIER-STOKES EQUATIONS UNSTEADY FLOW COMPUTATIONAL FLOW DEVELOPMENT Subject Category 34 19 Security Clasif. (of this reportl 20. Security Classif. (of this papa) 21. No. of Pages Price* 22.
UNCLASSIFIED UNCLASSIFIED 28 For sale by the National Technical Information Service. Springfield Virginia 22161