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Accommodations Rosochy (voivodeship kujawsko-pomorskie, county brodnicki)
Long may weekend Rosochy (voivodeship kujawsko-pomorskie, county brodnicki)
Long may weekend Rosochy (voivodeship kujawsko-pomorskie, county brodnicki)
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Also objects in the area 20 km
400–500 zł/group
Cottage in the forest
Bodzianka, Zbiczno
approximately 5,1 km
from the city/town centre
Regular offer
400–500 zł/group
Bodzianka - a detached holiday home located in Zbiczno in the Kuyavian-Pomeranian Voivodeship, 42 km from Grudziądz. House with terrace and two balconies, garden and views and access to Sosno Lake. Free private parking is available on site. Storey…
from 1 620 zł/total price
Picnic in the cottage Brda by the lake
Domki kempingowe nad jeziorem Sosno, Zbiczno
, zbiczno 212
approximately 7,1 km
from the city/town centre
Regular offer
from 1 620 zł/total price
BRDA - 1620 PLN Easter and Maya - 45 zlotys / person for the price of 1 boat, 1 canoe, 2 bicycles, grill wood and fireplace from Saturday 27/04/2019 at 09:00 to Sunday 05/05/2019 at 20:00 (9…
See other special offers from the area Rosochy
200–2 000 zł/room
Hotel Rondo, Wabrzezno
, ul. Mikołaja z Ryńska 11a
approximately 28,5 km
from the city/town centre
Regular offer
200–2 000 zł/room
In view of the numerous events that we can arrange the complex area, we offer several solutions for building in the form of conference rooms. Their decoration, setting tables and all the complex spatial will meet the expectations of each of our…
70–80 zł/a room
Summer holidays 2020
1 like
Agroturystyka Jelonek, Gorzno
, ok. Karw 10i
approximately 33,5 km
from the city/town centre
Regular offer
70–80 zł/a room
Room dwuosobowyz comfortable two beds,or with one 160/200m, bedside tables, wardrobe, coffee table, chairs,LED TV, radio, internet connection, bathroom, shower, mountain bikes at the disposal, Grill, Bonfire, terrace,sun lounge, parking, the…
400 zł/total price
Bachelorette party
1 like
Agroturystyka Jelonek, Gorzno
, ok. Karw 10i
approximately 33,5 km
from the city/town centre
Regular offer
400 zł/total price
House for rent in Górzno for 10-12 people. 5 rooms with the possibility of an extra bed, a 30 m living room, a terrace, a barbecue grill, silence, peace, fireplace, parking. More at…
from 350 zł/total price
Summer holidays 2020
1 like
Agroturystyka Jelonek, Gorzno
, ok. Karw 10i
approximately 33,5 km
from the city/town centre
Regular offer
from 350 zł/total price
House for rent on vacation for 10 persons, 5 double rooms, 4 bathrooms, kitchen, beauty 35m, terrace, grill, bonfire, world to barbecue,set,mountain bikes, parking,for children sandbox, swing. Possibility to buy food at breakfast - PLN 15/adult, the…
60–70 zł/a room
Last Minute offers
1 like
Agroturystyka Jelonek, Gorzno
, ok. Karw 10i
approximately 33,5 km
from the city/town centre
Regular offer
60–70 zł/a room
Double rooms available in June with 15% discount in price 60 PLN per room with one double bed or two single,bathroom, tv…
30–40 zł/os. (area)
For e-turysta website users
1 like
Agroturystyka Jelonek, Gorzno
, ok. Karw 10i
approximately 33,5 km
from the city/town centre
Regular offer
30–40 zł/os. (area)
5 double rooms, 3 with bathrooms, to room no. 3 and 4 is one bathroom. These are good rooms for families with two or more children because in pokju no. 3 is a sofa at a total creates accommodation for 6 people. Terrace, Grill, Bonfire, world to…
250–360 zł/os. (area)
God's body for a group of up to 10 people - package
1 like
Agroturystyka Jelonek, Gorzno
, ok. Karw 10i
approximately 33,5 km
from the city/town centre
Regular offer
250–360 zł/os. (area)
House for rent as a whole for a group of 10 -12 people. The package includes: 4 nights, 4 breakfasts, 1 lunch, 1 supper, 3 dinners Package price: 360 PLN adult, children under 3 years without benefits, children from 4 -14 years old - PLN 250. One…
to 220 zł/os. (area)
Weddings, communions, Baptisms
1 like
Hotel Kuźnia Smaków ***, Male Pulkowo
, Małe Pułkowo 20
approximately 28,5 km
from the city/town centre
Regular offer
to 220 zł/os. (area)
100–400 zł/room
1 like
Hotel Kuźnia Smaków ***, Male Pulkowo
, Małe Pułkowo 20
approximately 28,5 km
from the city/town centre
Regular offer
100–400 zł/room
110–130 zł/os. (area)
Corporate team building
1 like
Hotel Kuźnia Smaków ***, Male Pulkowo
, Małe Pułkowo 20
approximately 28,5 km
from the city/town centre
Regular offer
110–130 zł/os. (area)
85–220 zł/os. (area)
Weddings, Communions, Baptisms, Birthdays
Zajazd Karczówka, Rypin
, ul. Warszawska 142
approximately 39,8 km
from the city/town centre
Regular offer
85–220 zł/os. (area)
Our passion for gastronomy began in 1996, where the first place was the U Toniego Restaurant in the center of Rypin. Over the years, we tried to raise the standard of our services, therefore in 2002 a newly built gastronomic restaurant was…
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e-turysta.com project is a touristic social networking site presenting the accommodation and tourist offers from entire Poland. The accommodations can be searched by location criterion, i.e., by cities, geographical regions, historical regions and colloquial names of regions. The accommodation can also be found in a particular landscape, so you can search for accommodation at the seaside, in the mountains, by the lake, or in the country (also agritourism). e-turysta.com gathers also tourists interested in specific forms of spending free time in an active way and extreme sports lovers. Particular accommodation offers may correspond with the possibility of practicing specific sports such as sailing, gliding, rock climbing, or leisure activities such as hiking or trekking. The available accommodations are also divided into different categories of accommodation facilities. You can look for accommodation in hotels, spa resorts, holiday resorts, hostels, guesthouses, agritourist farms, as well as private lodgings, guest rooms or on campings.
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text: The Maurer Söhne company's main focus is on expansion joints and building components made of steel and rubber.Its structural protection systems help to avoid damage to structures caused by forces in motion, producing load transferring devices, which protect structures against overstress such as earthquakes. The company also designs structures for roller coasters and amusement rides. Report by Marion Hütter.

subset: commoncrawl


text:
Summit Appliance FF61BI 24 in. Freestanding Counter Depth Compact Refrigerator, White
$930.00 You Save $279.00 (30.00%)
Check Estimated Shipping Cost$
Sized with a 24" footprint, the FF61BI is front-breathing for built-in use. The fully finished cabinet also allows freestanding use for added versatility. This model has a white exterior finish. The reversible door includes a professional style handle in stainless steel.
The FF61BI refrigerator utilizes automatic defrost operation to ensure minimum user maintenance. The 5.5 cu.ft. interior offers more storage space than most models in this size class. Adjustable glass shelves ensure spill-proof storage, while a large crisper drawer is ideal for keeping produce at its best. A removable wine shelf lets you keep bottles securely in place. The door includes three storage racks for condiments and tall bottles. The seamless interior also features a dial thermostat and automatic light.
Designed and constructed in Europe, the FF61BI refrigerator offers reliable cold storage for any home looking to install a quality all-refrigerator under the counter. For additional finish options, browse the FF61BI Series.
Flexible design allows built-in or freestanding use in 24" spaces.Features
- Includes adjustable glass shelves for spill-proof storage
- Deluxe interior includes a scalloped wine shelf
- Door racks provide convenient storage options
- Automatic defrost ensures minimum user maintenance
- Full 5.5 cu.ft. capacity inside a convenient 24" footprint
- Finish: White
- Depth with Handle: 24.63" (63 cm)
- Depth with door at 90°: 45.38" (115 cm)
- Capacity: 5.5 cu.ft. (156 L)
- Defrost Type: Automatic
- Door: White
- US Electrical Safety: UL
- Canadian Electrical Safety: ULC
- Energy Usage/Year: 307.0kWh/year
- Amperage: 1
- Door Swing: RHD
- Reversible: Yes
- Crisper Qty: 1
- Crisper Cover: Wire
- Shelf Type: Glass
- Shelf Qty: 3
- Full Door Shelf Qty: 3
- Adjustable Shelves: Yes
- Wine Bottle Shelves: Yes
- Thermostat Type: Dial
- Fan Type: Exterior
- Refrigerant Type: R134a
- Refrigerant Amount: 1.7oz
- High Side PSI: 285
- Low Side PSI: 70
- Level Legs Qty: 4
- Interior Light: Yes
- Interior Height: 26.25" (67 cm)
- Interior Width: 21.0" (53 cm)
- Interior Depth: 18.0" (46 cm)
- Compressor Step Height: 5.5" (14 cm)
- Compressor Step Width: 21.0" (53 cm)
- Compressor Step Depth: 6.0" (15 cm)
- Country of Origin: USA
- Dimension: 33.25" H x 23.63" W x 23.0" D
- Weight: 110 lbs


text:
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Address : 7th K.M. khandwa-Khargone Road, Near Gayatri Mandir, Meharja
City : Khargone
Phone : 07282-284584
Mobile : 09827159156
Email : email@example.com
Website : http://shreejeetech.com/
In year 2010, ShreeJee Institute of Technology & Management was established. It is a premier institute of khargone in Madhya Pradesh. This institute is affiliated to Rajiv Gandhi Proudyogiki Vishwavidalaya (RGPV), Bhopal. Offered engineering courses by this colleges is approved by All India Council for Technical Education (AICTE), New Delhi and Govt.of M.P. Institute offers the 4 year degree courses in field of engineering.
Main aim of this institute is provide job oriented education to younger generation for a better future. Institute has a well experienced teaching staff.
Computer LAB with internet facility
Centeral Library
Cultural Activities
Training and placement cell.
Bus Facility
Under Graduate Courses:
B.E. (Electronics & Communication Engineering)
B.E. (Mechanical Engineering)
B.E. (Computer Science & Engineering)
B.E. (Civil Engineering)
B.E. (Electrical & Electronics Engineering)
Eligibility Criteria
B.Tech : Candidate should passed the H.Sc./10+2(academic stream)/ PET or equivalent with Maths, Physics & Chemistry from Madhya Pradesh state Board or from any other recognized Board or qualify MP pre Engineering Test (MPPET) i.e conduct by VYAPAM or candidate passed the AIEEE (All India Engineering entrance examination)exam that is conducted by Central Counseling Board (CCB).
Admission Procedure
Admission in B.E. Courses is based on online counselling conducted by DTE Bhopal as counselling authority. Seats are filled according to merit on basis of PET conducted by Vyapam Bhopal.
Other Important Information :
Director No . : 09407155004
Email ID : firstname.lastname@example.com
For Admission:- 09893577045
Address : Vivek Colony,Opp. Guna Airport
City : Guna
Phone : 07542 - 269140
Mobile : 09425010074
Email : email@example.com
Website : http://saeguna.org/
About Educational Institute
Sha-Shib Academy Private Limited is managed and run Sha-Shib Aerospace Engineering, Guna. ACADEMY OF AVIATION & ENGINEERING is Approved by Director General of Civil Aviation, Govt. of India for the following A.M.E. (Aircraft Maintenance..


text:
$5,995 5 bed 2 Van Gordon Place, Danville CA, 94526
Previously Listed $5,995 5 bed
2 Van Gordon Place, Danville, 94526
Commute to Downtown Danville
This apartment is in Danville. Nearby parks include La Vista Park, Hap Magee Ranch Park and Hap McGee Ranch Park.
2 Van Gordon Place has a Walk Score of 28 out of 100. This location is a Car-Dependent neighborhood so most errands require a car.
Move right in to this lovely 5 bedroom, 2.5 bathroom home! The house has been beautifully updated and has newer dual pane windows with wood blinds. This west side, single story rancher features wood floors throughout, and a great floor plan. You will love the large yards with 2 storage sheds, and nicely landscaped gardens. Pets negotiable with additional deposit.
Contact us to schedule a showing.
Pets allowed:
Owner/manager tools | Report bad listing | From homes.rently.com
Danville, California, 94526
Most errands require a car.
Explore how far you can travel by car, bus, bike and foot from 2 Van Gordon Place.
Bus lines:
21 BART Walnut Creek/San Ramon
0.2 mi
321 BART Walnut Creek/San Ramon
0.2 mi
321 Walnut Creek BART/San Ramon
0.2 mi
21 Walnut Creek BART/San Ramon
0.2 mi
View all Danville apartments on a map.
Popular apartment searches include pool, fireplace and hardwood floor.
Search for homes in Danville or find a Danville real estate agent who knows walkable neighborhoods. Links will open on our partner site Redfin.com.
2 Van Gordon Place is in the city of Danville, CA. Danville has an average Walk Score of 23 and has 42,039 residents.


text:
New to mala beads?
A mala is easy to use, and can be worn by anyone. People have used them for thousands of years as a tool to help focus the mind during meditation, mantras, or prayer. Others wear them as a beautiful piece of jewelry for the believed healing properties of the stones themselves, or as a simple way to remind them of their intentions, affirmations, or goals.
A good beginning practice that anyone can do with a
mala, is to take a few minutes each day to close your eyes, and take a slow deep breath with each bead. The goal is to give yourself a break, slow down, and learn to be present and peaceful in the moment.
Each mala is carefully handmade using quality materials. They are never rushed, and are infused with positive reiki energy before being placed inside their gift box.
For easy reference, the box includes printed information about malas, and a description of the beads used, and their meaning.
All malas come with a soft drawstring pouch to protect your mala when not in use.
- This mala is hand knotted on gray cord with genuine 8mm gemstones and rudraksha.
It measures approximately 23" from top to bottom, and has a dark gray tassel.
RUDRAKSHA: "Rud-ruck-sha." These seeds are from a tree which usually grows at a certain altitude in the mountains, mainly in the Himalayan region. They are the original Vedic "beads of power" worn by the Yogis of India and the Himalayas for thousands of years. Yogis and Monks have found that wearing the Rudraksha beads gave them a tremendous amount of tranquility and concentration, that helped them meditate for very long periods of time. Rudraksha is considered to be sacred and extremely powerful in manifesting.
Add a drop or 2 of your favorite essential oil to a rudraksha seed, and your mala becomes a diffuser!!
MOTHER OF PEARL: (white, cream) psaid to protects from negative influence, increase intuition, and promote creativity. It is also said to help our emotions become more balanced, and enable you to more easily express love. It is believed to bring clarity of thought in decision making and calm the mind.
LARVIKITE: a protective and grounding stone that is said to repel negative energy, stimulate creativity, and teach patience.


text:
Mark Waldman, an expert in neuroscience, shares with us some powerful tips and tricks to change our brain so to cope with anxiety, negative thoughts and stress and enhance self-esteem and productivity.
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The Canva City Project
The past few months, I have been watching Matt Miller from Ditch that Text Book, Lisa Johnson from Tech Chef 4 You and Tony Vincent of Learning in Hand and Shapegrams having their students create amazing stories using Google Slides, Google Drawings and Canva. As many of you know, I have been big fans and friends with all three and I'm always looking towards their social media and websites for inspiration for my own classroom. About a month ago, I saw that Canva had created their new Animated Social Media Posters, I knew I had to infuse this into my classroom, but I didn't know just how, but then inspiration hit me.Continue reading "The Canva City Project"


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It is one of the biggest names in humor – but you probably never heard it.
Photographer Marcus Russell Price is touring Amy Schumer, regularly in Pete Davidson's "SNL" dressing room and includes Dave Chappelle. It is given to him, and his lens, access to list A.
"I have seen the jokes from birth until they hit the stage," said Price with An Post.
It all started when a resident of Fort Greene – who had one photographic class in a high-comic school Hannibal Buress met in 2011, started to hit him with the others.
"I have never considered photography as a career until I liked Hannibal with my photos," said Price, 35, who was working as a graphic designer at the time and who is now installing his work @marcusrussellprice on Instagram.
"You see old photographs of people like Richard Pryor and you like,' Thank you that God was there to take that picture, "Price said. "I am that person now." T
Here are the stories behind some of his favorite.
Aziz Ansari in Mumbai
During Ansari's first trip to India – his family's home country – last May, "he felt the rows were not focused on the trip," Price said.
Both of them spent their time running on the streets of Mumbai and Delhi. "It was almost as we were on vacation together."
They were busy exploring spices, food and textile markets in Mumbai when their friends focused on them. "He went around, for example, tú Where do you want to go to us? 'And I took the shot,' Price said.
Amy Schumer on tour
Schumer's 2016 global tour was the first time she had been playing locations. "There were thousands of people every night. It was a great experience, "Price said.
After each performance, the photographer had the lights of the house to bring Schumer's spectacular shooting to his audience. But when the Long Island girl played Madison Square Garden, the crowd joined the crowd. "She went around and gave me this look," Price said.
Pete Davidson at home
"Pete keeps a very tight circle," Price said. "I don't have access to most people." .
"One of his favorite things is to relax, smoke, see films and get a tattoo," Price said. "I think he was getting unicorns."
He added that Davidson is getting out of the skin: "Recently, he's going over the tattoos. Covering envelopes, they are only overlapping. "
More photos of enthusiastic friends Price
(TagsToTranslate) Entertainment (t) amy schumer (t) aziz ansari (t) comedy (t) pete davidson (t) photography


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Mr. Leach. I appreciate that. I just want to stress that from a congressional perspective, there is no desire of this Congress that I know of anywhere to downgrade a commitment, and that we are fully behind the maintenance and upgrading of our commitment to the Pacific. And we respect the discretion of the Executive Branch to rearrange the forces as it thinks is most effective. That is the only point I am trying to make.
There is a new geopolitical strategy, however, that is worthy of serious review, and that applies to DoD in particular, as well as to the responsibilities of the Navy. That relates to the new Proliferation Security Initiative which could involve some sort of interdiction in trade, particularly of illicit weaponry, particularly stemming from North Korea. I am wondering if either you, Mr. Rodman, or Admiral Fargo can explain how this initiative will work. And then have you thought through the international legal dimension in terms of will you be seeking new international legal rationales or sanctions in this arena?
Mr. Rodman. Well, let me start on that, and my colleagues can elaborate. This is only at the early stages of development. This is an initiative that the President broached in his Krakow speech. There was a meeting in Madrid a few weeks ago of the countries that are interested in it, and I think as it stands now, it includes a number of components. It is countries looking at their own national authorities under which they can take practical steps to tighten restraints on this kind of commerce in WMD, to look at export control regimes, for example, but certainly it does—there was a Madrid statement on June 12th which did explicitly refer to, "proactive measures to interdict shipments." That involved some new—certainly some new practices, and I think one—my sense is that it is something that we might, for example, raise at the U.N. Security Council, but there may be other forums as well in which we would develop some multilateral consensus on new measures. That is my understanding of where we are heading.
Mr. Leach. Secretary LaFleur, do you want to comment on that?
Mr. Lafleur. I think Secretary Rodman has laid it out fairly clearly. We are at a preliminary stage in this discussion, and I don't think we have reached any conclusions yet about what we will need in the way of
Mr. LEACH. Clearness is lack of clarity.
Admiral Fargo.
Admiral Fargo. Mr. Chairman, let me just address it from the operator standpoint, and certainly this is the kind of initiative that would produce the kind of architecture that we would certainly look forward to from the standpoint of being able to execute a maritime interdiction operation against not only drugs, but proliferation as well as terrorism. So this, I think, has great potential to close up some of the seams that we see within the international spectrum that are there right now, that we need to address to ensure that illegal activity can't exist.
Mr. Leach. Let me just conclude with one question before turning it over to Mr. Faleomavaega. Secretary LaFleur commented on our looking carefully and watching Japanese legislation. We also, in reference to Admiral Fargo, note the commitment of the United States Navy to the area of the Taiwan Straits, and that this is an area that could have potential explosiveness if the situation isn't handled steadily and correctly.
And Admiral Fargo made reference to the dual obligations or the dual assumption of American foreign policy being rooted in the one China policy since the Administration of Mr. Nixon, but also in reference to the Taiwan Relations Act, which implies that we don't want to see the status of Taiwan change by use of force.
I have always thought that—as I discussed it yesterday with Admiral Fargo, that there is in international affairs two words that are usually synonymous, that being self-determination and independence, but that in Taiwan you have the one place in the world where they are juxtaposed, that Taiwan can have a maximum degree of self-determination if it does not declare independence. If it declares independence, that self-determination will be immediately placed in jeopardy, and the United States will be involved in ways that could be very stark.
And so it is my understanding that there are some initiatives in Taiwan to seek referendums on an independence movement that our AIT in Taiwan has suggested this might be unhelpful, and so I would like to make it clear that is it the position of the United States Government that looks to support, or is it apprehensive about an independence movement on Taiwan? And it is my understanding that this is inconsistent with U.S. policy. Is that correct? For Secretary LaFleur.
Mr. Lafleur. We, of course, maintain fully our obligations under the Taiwan Relations Act. We also, of course, do not support Taiwan independence.
Mr. LEACH. That is the Department of Defense's position as well? Secretary Rodman.
Mr. RODMAN. It is the President's position and the position of the Administration that that has to change. As you said yourself, there has been continuity, I think, over several Administrations on these principles.
Mr. LEAch. And this is the way that the Department of the Navy looks at it as well. Is that right, Admiral Fargo?
Admiral Fargo. Yes, sir. It is fully consistent.
Mr. Leach. Fine. Thank you very much.
Mr. Faleomavaega.
Mr. Faleomavaega. Thank you, Mr. Chairman, and thank the witnesses for their testimony this afternoon.
I just wanted to ask Admiral Fargo, as I mentioned, that you have a military command that spans for some 100 million square miles, and I am curious what does this mean for soldiers and sailors? How many soldiers and sailors are under your command?
Admiral FARGO. There is a little over 300,000.
Mr. FALEOMAVAEGA. How many ships are under your command
Admiral FARGO. The ship count is in the neighborhood of 160 today.
Mr. Faleomavaega. One hundred and sixty? I thought it was 230 at that last count that I had. Maybe not.
And do you foresee—and maybe Secretary Rodman could also be helpful to me. Do you foresee any restructuring of CINPAC, the way it is now composed? Do you see—because it seems that the magic word being taken by the Administration is flexibility, and I am just curious how flexible is CINPAC Command if it comes to any major conflict that we have in the Asia-Pacific region? In your opinion, Admiral Fargo, will you have the flexibility to deal with any given situation in the region?
Admiral FARGO. Congressman, I think I have got clear flexibility, and that is kind of the hallmark of our forces and the hallmark of our strategy.
Mr. Faleomavaega. Sweet and short. I like that.
There was an announcement, I think. Under Secretary Wolfowitz had made an announcement that it was the intention of the Administration to relocate some 37,000 soldiers currently stationed in South Korea further south, I guess, away from the DMZ. What seems to be the reaction of the South Korean Government to this? It seems like it implies that we seem to be running away from our responsibility to shoulder with the South Korean forces if there should be a conflict or if there should be an invasion from the North Korean Army. Can you comment on that, Mr. LaFleur?
Mr. Lafleur. Sir, we have explained in some detail to the Republic of Korea's government our intentions with respect to the movement of the bulk of our forces from their current locations north of Seoul largely into two new hubs to be located around existing facilities further south.
The logic here, I think, is very clear, and I think the Koreans have come to understand what our approach is and to support it. And the logic is that given our new capabilities, the opportunity to further enhance the mobility of our forces and the requirement to be able to deploy our forces rapidly, it makes much more sense to have them repositioned and located in other facilities from which such deployment is possible. In their present locations, north of Seoul, they run into a number of logistical problems in terms of their ability to move rapidly, since these facilities were largely designed for another era of warfare.
But in addition, over some 50 years that we have had many of these facilities, the city of Seoul and surrounding communities have expanded dramatically, and if you fly today overhead over those facilities, you will see the encroachment of new communities around our facilities, which makes it very difficult to maneuver, makes it difficult to train. So moving those forces to new locations, concentrating them, we think, will actually enhance our ability to deter aggression on the Korean Peninsula, as well as to reduce further any possibilities for incidents or frictions.
Mr. Faleomavaega. So you are saying it is mainly because of congestion and logistics and not because of lack of commitment on our part to be part of the defense structure that we have there in defending the South Korean people?
Mr. Lafleur. It is absolutely not because of lack of commitment. As a matter of fact, a few days before our last round talks, General LaPorte, the Commander of United States forces in Korea, reviewed for the Korean public the some $11 billion in investments in our capabilities that we intend to make in our forces in South Korea in the years ahead. So what we are indicating is that we want to move our troops into enduring facilities so that we can sustain the alliance for the long term.
Mr. Faleomavaega. Our security agreement with Japan—and this always seems to be a sticky issue every time. I am talking about Okinawa, and looking at it, it is about as far as away from Japan as you could ever get it, and I am curious if relations between the locals—always the problems dealing with our Marines there—and our Marine force structure there. How many are stationed there in Okinawa?
Mr. LAFLEUR. About 20,000.
Mr. Faleomavaega. And do you see that our presence in Okinawa is just as vital in that area? Do we really need to be in Okinawa?
Mr. Lafleur. My colleagues may want to comment from their perspective. I think from ours, indeed Okinawa occupies a strategic position in the region, and I think from our point of view, it will continue to do so for many years to come.
Mr. FALEOMAVAEGA. Secretary Rodman or Admiral Fargo.
Mr. Rodman. Just briefly, we and the Japanese Government and the Okinawa authorities are looking at adjustments of our presence in Okinawa. As Chris LaFleur said, in the Korean case we want to—there may be ways to have a military presence that is less of a burden on the local population and yet also gives us more flexibility. So we are looking at adjustments, and we have been for a number of years, involved with the Japanese on ways of perhaps realigning our forces there, but we don't expect to leave there. I think we are talking about small adjustments.
Mr. Faleomavaega. The reason why I raise the issue is that I believe the Japanese Government is second only to our government as far as spending on its military capabilities, and maybe you could correct me on that, Admiral Fargo. Is it true that Japan is second only to the United States in spending on its military defense forces? And for that reason, why should we be in Okinawa if the Japanese can defend themselves in that regard?
Admiral Fargo. Well, I can't speak to what the Japanese are spending on their own military forces in a precise number. I can tell you that the host nation assistance the Japanese provide to us is in the neighborhood of $4.7 billion. So it is very substantial.
And so to get back to the fundamental question, certainly, as Secretary Rodman said, you know, we are always looking at the appropriate adjustments with the Government of Japan, but those forces—those marine forces and air forces on Okinawa are absolutely central to our planning and our ability to meet our security concerns in the Pacific.
Mr. Faleomavaega. Thank you, Mr. Chairman. I know my time is up.
Mr. Leach. Mr. Bereuter.
Mr. Bereuter. Thank you, Mr. Chairman.
Secretary Rodman, in light of the North Korean nuclear development program and their ongoing missile development program, what measurement of concern and interest would there be in Japan on a missile development program? And what would be some assessment of how the Japanese people may have a changing attitude on this, if at all?
Mr. Rodman. In offensive missiles or
Mr. Bereuter. Defensive.
Mr. Rodman. Defense. This is, as you know—we have had a robust R&D program with the Japanese over the years, and they are now approaching a decision on how to carry that forward. And they haven't yet made a decision, but I think there was a hint in the President's—the joint statement of the President and Prime Minister Koizumi that they are approaching making a decision, and I think you can expect, given the nature of the threat, that they are quite interested in pursuing missile defense.
Mr. Bereuter. Is there a time line for their decision that has been announced?
Mr. Rodman. I don't know if it has been announced. I think it will be soon. I don't know anything more specific than that.
Mr. Bereuter. I think it was you, perhaps, Mr. LaFleur, that first mentioned the Yongsan base in Seoul. This has been on the agenda for quite some period of time; I think since 1991 formally it has been considered. My understanding has always been that we were willing to leave that facility if an adequate replacement was made available to us, and that there would be a significant financial contribution from the Republic of Korea for us to make that move. Has there been any retreat from that understanding? Are we any closer to having a commitment of how much Korean currency will be generated for that purpose?
Mr. Lafleur. Sir, we have, in fact, had some considerable discussion on what would be needed to move our forces out of Yongsan into new facilities located around and alongside some of our existing facilities further south, notably Osan Air Force Base. And indeed the Korean Government has indicated that they are prepared to move forward to try to procure additional land that we would need in order to realize that relocation. Finally, and as a demonstration of this, they are looking to make a rather substantial increase in their defense budget
Mr. Bereuter. May I simply express to you a concern that they do, in fact, make a significant contribution. That contribution ought to be substantial, and you ought to push hard on that.
Is there any evidence, Secretary Rodman and Mr. LaFleur, of a change in the sunshine policy which was enunciated by previous President Kim? Is there any change noticeable?
Mr. Rodman. The sunshine policy? No. I think the new President is of the same party and has the same philosophy, and this is something we discuss with him on a regular basis.
Mr. Bereuter. Would you agree, Mr. LaFleur? Is that your assessment?
Mr. Lafleur. I think that is broadly true. Certainly events have evolved since the new President has taken over, and I think in our discussions with the Republic of Korea, both at the summit level on down, and also in partnership with the Japanese, we have all agreed that we also need to take a firm approach with North Korea.
Mr. Bereuter. Thank you.
Admiral Fargo, you mentioned the IMET program in specific reference to Indonesia and the consultations that may go on. I would ask you the breadth of those consultations, and how you will proceed in DoD to do that.


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KIEL, Germany – Petty Officer 2nd Class Stephanie Jaskolski, a native of Black Creek, Wisconsin, is participating in the Baltic Operations (BALTOPS) exercise with 18 other nations.
"I am looking forward to interacting with other countries and their militaries during BALTOPS," said Jaskolski.
BALTOPS 2019, scheduled for June 8-21, includes sea, air and land assets. The multi-national exercise provides a unique training opportunity that fosters cooperative relationships critical to ensuring safety at sea and security on the world's interconnected oceans.
Jaskolski is an information systems technician aboard the USS Mount Whitney.
Mount Whitney serves as the Command Ship for Commander, SIXTH Fleet/ Commander, Joint Command Lisbon/Commander, Striking Force NATO and has a complement of 150 enlisted personnel, 12 officers and 150 Civilian Mariners from Military Sealift Command.
BALTOPS 2019 was planned and is being led by U.S. 2nd Fleet (C2F), as directed by U.S. Naval Forces Europe. C2F was re-established last summer as a response to the changing security environment, and BALTOPS 2019 marks the first time the renewed fleet will be operating in Europe.
Commander, C2F, Vice Admiral Andrew "Woody" Lewis, will lead the exercise on behalf of U.S. Naval Forces Europe.
"As you all are aware, U.S. 2nd Fleet will be leading the exercise, but make no mistake, it will be founded on NATO and partner principles," said Lewis. "Through BALTOPS 2019 and exercises like it, we strengthen our relationships and improve overall coordination and interoperability between allies and partners during both peace and times of conflict."
The exercise will begin in Kiel, Germany, with the pre-sail conference. At-sea training will occur throughout the Baltic Sea, including events scheduled near Putlos, Germany; Saaremaa Island, Estonia; Riga, Latvia; Klaipeda, Lithuania; and Ravlunda, Sweden. At the end of the exercise, most participating ships will sail to Kiel, Germany, to participate in the Kielerwochen Festival (Kiel Week).
Allied nations with ships and forces participating in BALTOPS 2019 include Belgium, Denmark, Estonia, France, Germany, Latvia, Lithuania, the Netherlands, Norway, Poland, Portugal, Romania, Spain, Turkey, the United Kingdom, and the United States. NATO partner nations Finland and Sweden will also participate in the exercise.
Serving in the Navy means Jaskolski is part of a world that is taking on new importance in America's focus on rebuilding military readiness, strengthening alliances and reforming business practices in support of the National Defense Strategy.
"Our priorities center on people, capabilities and processes, and will be achieved by our focus on speed, value, results and partnerships," said Secretary of the Navy Richard V. Spencer. "Readiness, lethality and modernization are the requirements driving these priorities."
Though there are many ways for sailors to earn distinction in their command, community, and career, Jaskolski is most proud of receiving a Navy and Marine Corps Achievement Medal for providing off-duty emergency medical care.
"I am a registered nurse and I do that by trade," said Jaskolski. "It was an opportunity to bring my nursing skills to what I do in the Navy."
As a member of one of the U.S. Navy's most relied upon assets, Jaskolski and other sailors know they are part of a legacy that will last beyond their lifetimes contributing to the Navy the nation needs.
"Serving in the Navy means giving back to my country, learning leadership, experiencing diversity and expanding my horizons," said Jaskolski.
By Mass Communication Specialist 2nd Class
Theodore Quintana
Black Creek native participates in multinational exercise in Baltic Sea region
KIEL, Germany – Petty Officer 2nd Class Stephanie Jaskolski, a native of Black Creek, Wisconsin, is participating in the Baltic Operations (BALTOPS) exercise with 18 other nations.


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Joint Replacement
Bourck D. Cashmore, M.D.
Dr. Cashmore In The News
Tammy Doering, PA-C
Tammy Doering, PA-C NAO has been fortunate enough to have Tammy on its provider team since 2007. She obtained her master's of Physician Assistant Studies from the University of St. Francis in Illinois, in 2005, which she left Flagstaff for to attend. Other than that time, Tammy has lived in Flagstaff since 1992. It was Flagstaff where Tammy obtained her bachelor's in Zoology from Northern Arizona University. Tammy is a member of the American Academy of Physician Assistants (AAPA), Arizona State Association of PAs (ASAPA), and Physician Assistants in Orthopaedic Surgery (PAOS). She is currently providing care to patients needing shoulder and knee care inside the Sports Medicine Center at NAO. When she is not at work, she enjoys spending time with Read More
Greg Harris, PA-C
Greg Harris PA-C Greg is an expert Physician Assistant at Northern Arizona Orthopedics in Flagstaff, Arizona. He received his bachelor's degree from the University of Tennessee and then worked in cancer research at Vanderbilt University, eventually receiving a master's in Cell Biology. He went on to graduate from Trevecca Nazarene University in Nashville, Tenn. with a second M.S. degree in the Physician Assistant program in 2002. He worked in general orthopedics in west Tennessee before moving to Flagstaff in 2006. He currently resides in Flagstaff with his wife Lynn and one son. He enjoys hiking, cycling, and photography. Greg currently provides care to patients in the Arthritis and Fracture Care Center.


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ED to appeal against bail to Ratul Puri
Opposing Puri's bail, the agency had told the special court that on receipt of fresh information gathered from its probe, the Indian govt has shot off letters rogatories to different countries on November 21. ED had told the court that "numerous documents" pertaining to the chopper case were burnt by Puri and "bags of documents were shifted by him to thwart the investigation".
NCLAT directs ED to file final affidavit in BPSL assets attachment matter
A two-member NCLAT bench headed by Chairperson Justice S J Mukhopadhaya also asked the ED to clarify about its role after the attachment of assets of Bhushan Power and Steel Ltd (BPSL). The NCLAT has directed to list the matter on December 12 for the next hearing. The appellate tribunal was hearing a batch of petitions, against the attachment of BPSL assets.
Discounts in market are not sustainable for the co: ED Shashank Srivastava, Maruti Suzuki
The country's largest car maker Maruti Suzuki India on Tuesday said it will increase prices of its vehicles from January to offset rising in...
ED questions former Haryana CM Hooda in Chandigarh in money laundering case probe
The federal agency is probing Hooda's role in multiple criminal cases of money laundering, including the Manesar land case and the Associated Journal Limited (AJL) land case.
Chidambaram gets bail from SC in INX Media case, to walk out of Tihar jail
After 105 days behind bars in the INX Media case, former union minister P Chidambaram will now be out on bail.
28 bn and counting: Drake declared Spotify's most streamed artist of the decade
'Senorita' by Camila Cabello and Shawn Mendes, is 2019's most-streamed song.
INX Media scam: ED opposes P Chidambaram's bail plea in SC
Solicitor General Tushar Mehta, appearing for the Enforcement Directorate (ED), told a bench headed by Justice R Banumathi that economic offences are grave in nature as they not only affect the nation's economy but also shake people's faith in the system.
Bank fraud: Ratul Puri moves bail plea, court seeks ED's response
Special judge Arvind Kumar issued notice to the ED and directed it to file a reply by November 30.
BPSL acquired Rs 27,559-crore assets by diverting loans: ED
The agency has said BPSL acquired land valued at about Rs 361 crore, made addition of buildings valued at Rs 7,473 crore and plant and machinery of Rs 19,725 crore between 2011 and 2017. The funds infused as equity capital by the Singals and associated promoter companies were sourced from bank loans that were illegally diverted.
ED says HC order stopped it from arresting Karti Chidambaram in INX Media case
The ED is prosecuting the former minister also on charges of money laundering over an alleged Rs 10 lakh bribe paid to a shell company with connections to P Chidambaram's son, Karti.
ED appellate body yet to get chairman
No formal order/notification with regard to appointment of the new chairman has been issued so far. Justice Sunil Gaur, the retired Delhi High Court judge who had rejected the bail plea of former finance minister P Chidambaram in the INX media case, was reportedly tipped to be the new head of PMLA Appellate Tribunal.
Waiting to arrest Karti Chidambaram in INX Media case, ED tells Supreme Court
As the Supreme Court on Thursday heard the appeal of Congress leader P Chidambaram challenging the Delhi High Court order refusing to grant ...
RFL scam: Delhi HC sends ex-Fortis Healthcare promoter Malvinder to ED custody till November 28
The Delhi high court on Wednesday allowed the Enforcement Directorate (ED) to conduct custodial interrogation till Thursday of former Fortis Healthcare promoter Malvinder Singh and another co-accused to confront them with voluminous documents and several witnesses in a money laundering case related to alleged misappropriation of funds at Religare Fivest Ltd (RFL).
Terror funding: ED takes possession of Rs 6.20-crore assets of Kashmiri businessman
The Enforcement Directorate case against Watali relates to its terror funding and money laundering case against Hafiz Saeed, the founder of terror group Lashker-e-Taiba (LeT), and others.
Copyright © 2019 Bennett, Coleman & Co. Ltd. All rights reserved. For reprint rights: Times Syndication Service


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By Lassiter Strome. Kitchen Cabinets. At Monday, July 01st 2019, 02:57:54 AM.
If you are unsure which choice would best suit your kitchen, ask for numerous different paint swatches or cabinet door options before you install your new cabinets. Watch the light play on the different cupboards until you find the shade which suits your kitchen.
For a kitchen remodel, the kitchen will be fully stocked with cabinets, appliances, flooring, and more. In this instance, you are dealing with far less square footage than in an empty room. Cabinets take up a majority of the wall space. One method is to imagine that it is an empty room and buy enough paint to cover all walls as if it were an empty room. The extra paint can be saved for those inevitable touch ups.
Some designs focus on the kitchen island and paint it differently than the rest of the kitchen. However, other designs choose accent areas for a different color.The purpose of 2 color kitchen cabinets is to point out a specific part of the kitchen, add interest to this area and make it more comfortable to spend time in.
Inside developers generate an illusion of space with illumination under and under the cabinets. The correct lighting can make your kitchen bigger and more attractive. Lighter glass door color cabinet gives the look of more room. Tiles can be diagonally positioned on the floor. Designed hardware floors of the kitchen can be used in a galley and still offer the room a big look. If doing a modern small kitchen design and an island is desired, it is best to double it up as a work space as well. There are island designs that come already available and can suit your needs and preferences. The islands provide solutions to and space problems in your small kitchen.
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Узнать больше о подписке Scribd
Откройте для себя все, что может предложить Scribd, включая книги и аудиокниги от крупных издательств.
Altair Engineering, Inc., World Headquarters: 1820 E. Big Beaver Rd., Troy MI 48083-2031 USA Phone: +1.248.614.2400 • Fax: +1.248.614.2411 • www.altair.com • email@example.com THEORY Version 10.0 CONTENTS
20-jan-2009 1 Chapter
20-jan-2009 2RADIOSS THEORY Version 10.0 ALE FORMULATION
The derivative of any physical quantity can be computed either following the material point or following the gridpoint. They can then be related to each other.Given that F is a function f of space and time representing a physical property:The spatial domain is given by f(x,t).The material domain is given by f*(X,t).The mixed domain is given by f**( ξ , t).
20-jan-2009 3RADIOSS THEORY Version 10.0 ALE FORMULATION
∂f ∗ ∂f ∂f ∂x j ∂f ∂f (x, t ) = + × = + V j ( xk , t ) EQ. 220.127.116.11 ∂t ∂t ∂x j ∂t ∂t ∂x j X X X X t
∂f ∗ ∂f ∗∗ ∂f ( x, t ) = ξ + (V j − W j ) EQ. 18.104.22.168 ∂t ∂t ∂x j X t
⎛ ∂vi ∂σ ij ⎞ ∫ Φ ⎜⎜ ρ − − ρbi ⎟dV = 0 ⎟ EQ. 18.104.22.168 ⎝ ∂t ∂x j I V ⎠where F I = the weight functions ρ = Material density v = Velocity σij = Stress Matrix bi = Body acceleration vector V = VolumeThis can be rewritten in a form similar to the explicit Lagrangian formulation with the addition of a new nodalforce ftrm , accounting for transport of momentum:
∂ M ∂t { } { } { v = F ext − F int + F bod + F hgr + F trm } { } { } EQ. 22.214.171.124
where {F }= ∑ f trm trm
ηI = Upwind factor
20-jan-2009 4RADIOSS THEORY Version 10.0 ALE FORMULATION
∂vi FiItrm = (1 + η I )ρΦ I (w j − v j ) V EQ. 126.96.36.199 ∂x j
The upwinding technique is introduced to add numerical diffusion to the scheme, which otherwise is generallyunder diffuse and thus unstable.
⎡ ∂Φ I ⎤ η I = ηsign ⎢ (v − w j )⎥ EQ. 220.127.116.11 ⎣⎢ ∂x j j ⎦⎥
∂ρ ⎛ ∂ρ ⎞ ∂v ξ − ⎜⎜ (wi − vi ) ⋅ ⎟⎟ + ρ K =0 EQ. 22.214.171.124 ∂t ∂xi ∂xK t t ⎝ ⎠Applying a Galerkin variation form for the solution of equation 184.108.40.206:
⎛ ∂ρ ⎛ ∂ρ ⎞ ∂v ⎞ ∫ψ ⎜⎜ ∂t ξ − ⎜⎜ (wi − vi ) ⋅ ⎟⎟ + ρ K ⎟=0 ⎟ EQ. 22.214.171.124 ∂xi ∂xK t t V ⎝ ⎝ ⎠ ⎠where ψ = Weighting function
20-jan-2009 5RADIOSS THEORY Version 10.0 ALE FORMULATION
where ψ =1 ρ = constant density over control volume VTherefore: ∂ρ ∂vK ∫ ∂t dV + ∫ ρ ∂x V V K dV = 0 EQ. 184.108.40.206
ρdV = ∫ ρ (w j − v j )n j dS d dt V∫ EQ. 220.127.116.11 S 1442443 mass flux
This formula is still valid if density p is not assumed uniform over volume V.The mass flux across a surface is shown in Figure 1.3.1. Figure 1.3.1 Mass Flux
ρI + ρJIf η = 0 , there is no upwind. Therefore: ρ i = 2If η = 1 , there is full upwind.The smaller the upwind factor, the faster the solution; however, the solution is more stable with a large upwindfactor.
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∂ρe ⎛ ∂ρe ⎞ ∂v − ⎜⎜ (wi − vi ) ⋅ ⎟⎟ + (ρe + ρ ) K = 0 EQ. 188.8.131.52 ∂t ⎝ ∂xi ⎠ ∂xKwhere e = Internal energy in Joules (Nm) p = Fluid pressureApplying a Galerkin variation form for the solution gives:
⎛ ∂ρe ⎛ ∂ρe ⎞ ∂v ⎞ ∫ψ ⎜⎜ − ⎜⎜ (wi − vi ) ⋅ ⎟⎟ + (ρe + ρ ) k ⎟=0 ⎟ EQ. 220.127.116.11 V ⎝ ∂t ⎝ ∂xi ⎠ ∂xk ⎠Making the following assumptions:ψ =1ρe = constant over control volume VEquation 126.96.36.199. reduces to: ∂ρe ∂v ∫ dV + ∫ (ρe + ρ ) k dV = 0 EQ. 22.214.171.124 V ∂t V ∂xkApplying the divergence theorem gives: ∂ρe ∂v ∫ dV + ∫ (ρe(v j ⋅ n j )dS ) + ∫ ρ k = 0 EQ. 188.8.131.52 V ∂t S V ∂xkHence: ∂v ρedV = ∫ ρe(w j − v j )n j dS − ∫ ρ k dV d ∫ dt V S V ∂xk EQ. 126.96.36.199
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ALE MaterialsLaw Number Description Elasto-plastic2 /MAT/PLAS_JOHN Elasto-plastic-Hydrodynamic3 /MAT/HYDPLA Johnson Cook4 /MAT/HYD_JCOOK Hydrodynamic Viscous6 /MAT/HYD_VISC Rock Concrete Foam10 & 21 /MAT/LAW10 or /MAT/DPRAG Elasto-plastic with Damage22 & 23 /MAT/DAMA or /MAT/LAW23 Bimaterial20 /MAT/BIMAT Hydrodynamic - Bi-phase liquid gas37 /MAT/BIPHAS Boundary - Stagnation conditions in flow calculations11 /MAT/BOUND Gray model - Multiphase Gray E.O.S + Johnson's shear law16 /MAT/GRAY Thermal conductivity, purely thermal material18 /MAT/THERM
For the rest, refer to the next version of the theory manual.
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1 Figure 1.7.1 Flow Chart
When a Lagrangian formulation is used, the values of wj and vj are equal. Thus, EQ. 126.96.36.199 is equal to zero.
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⎛ ∂Φ I ⎞ η I = ηsign⎜⎜ (v − w j )⎟ ⎟ EQ. 184.108.40.206 ⎝ ∂X j j ⎠Development of a less diffusive flux calculation is currently under investigation. ∂Φ I Fi I = σ ij ∫ dV EQ. 22.214.171.124 V ∂X jThis option is activated with the flag INTEG (only in the CFD version).
1.10 StabilityThe Courant condition (neglecting viscosity effects) is used to determine the stability of an ALE process. Themaximum time step is calculated by: Δl Δt ≤ k EQ. 18.104.22.168 c+v−wwhere k = coefficient Δl = Smallest characteristic length of an element c = Material speed of sound v = Material velocity w = Grid velocityThe speed of sound is determined by:
1 ∂ρ 4 μ c= + EQ. 188.8.131.52 ρ ∂ρ 3 ρwhere ρ = Density μ = Dynamic viscosity p = PressureThe relative velocity between the material and grid motion (v-w) is computed by:
∑∑ (v ) 3 1 N 2 v−w= i I − wiI EQ. 126.96.36.199 N i =1 I =1
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Option 2:Velocity is set to minimum absolute velocity of master nodes.
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WM 1 < WM 2 WNI = WM 1 if EQ. 22.214.171.124
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ΔT0 = typical time step (Must be greater than the time step of the current run.)0 < γ < 1 = Nonlinearity factorη = Damping coefficientv= Shear factor (stiffness ratio between diagonal springs and springs along connectivities)This formulation is the best of the three, but it is the most computationally expensive.
This interface allows Lagrangian elements (structure) to interact with ALE (Arbitrary Lagrangian Eulerian)elements, which model a viscous fluid. Full slip conditions are applied at the boundary between the twodomains.The acceleration of the Lagrange node is computed by: r r r Fl + Fa γl = EQ. 188.8.131.52 ml + ma
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The normal material velocities of Lagrange and ALE nodes are equal. Therefore: r r r r va ⋅ n = vl ⋅ n EQ. 126.96.36.199
A gap is required for the wall, Figure 1.14.1. When a slave node distance to the rigid wall is within the gap: • Nodes are forced onto the rigid wall and set as Lagrangian. • Zero volume elements are emptied into neighboring elements and deleted.In addition to the information explained above, an ALE rigid wall definition requires the number of nodesimpacting simultaneously to be defined, along with the order of slave node impact.
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1.15 ExampleA typical application of the ALE method is using high velocity impacts. Below, a cylinder, moving at 227 m/s,impacts with a rigid wall. The material is copper, with a yield stress of 400 MPa. The initial diameter is 6.4 mmand initial length is 32.4 mm. The simulation was performed using two different methods: ALE and standardLagrangian. The results can be seen in Figure 1.15.1. Figure 1.15.1 Cylinder Impact Deformation
It can be seen that the cylinder mesh using ALE remains regular, unlike the Lagrange method, where largeelement deformation creates very small and skewed elements. This reduces the time step, leading to more timestep cycles. However, each ALE cycle takes longer than a Lagrangian.
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A classification of Aero-Acoustic problems can be made using the following three categories: • External wind noise transmitted to the inside through a structure: In the automotive industry, a pillar, side mirror and windshield wipers noise are typical problems of this category. • Internal flow noise transmitted to the outside through a structure: Examples of this class of problems are exhaust, HVAC and Intakes noises. • Rotating machines noise: Axial and centrifugal fans are noisy components that bring with them many interesting Aero-Acoustic problems.
Most of the Aero-Acoustic R&D works are performed experimentally but this method has some critical pitfalls.Although it is relatively simple to setup a microphone, measure a noise level and derive a spectrum at any givenlocation in space, the correct analysis of an Aero Acoustic problem involves the use of advanced experimentaltechniques and is complex to use. The Aero Acoustic engineering community seeks more and more the help ofCAE tools as they become available. Those tools complement the experimentations and allow a thoroughvisualization and understanding of the pressure and velocity fields as well as the structural vibrations.Furthermore, parametric studies can be carried out with little added cost since a numerical model modification isoften straightforward and the CPU time is becoming cheaper and cheaper.
CFD codes are available since over several years, able to predict with a reasonable precision steady state flows(drag and lift) and slow transient flows like heating and defrosting. Highly transient flows involved in the Aero-Acoustic phenomena have not been treated since they were not in the bulk of the needs and they required waytoo much CPU to be industrially feasible. Acoustic Propagation numerical tools have also been industriallyavailable since quite a few years. These tools operate in the frequency domain and are able to propagate a givenboundary condition signal in a fluid at rest, including the noise reflections, diffractions, transmissions andattenuations thanks to the various geometrical obstacles and different materials.
Attempts have been made to combine existing CFD and Acoustic propagation tools to predict Aero-Acousticproblems. Most methodologies are based on the Lighthill &Curle method, developed in the mid 50's and FfowcsWilliams & Hawkings contributions made in the late 60 's [67], [68], [69], [70]. The ideas underlying thesemethods are to decouple the flow pressure field and the acoustic pressure field. The fluid flow can then becomputed by a standard CFD code and the noise derived from the curvature and turbulent intensities of the flow.A propagation tool is then used to compute the noise on a sub grid of the CFD computational domain loosingtherefore quite some local information and high frequency content. First attempts were made withincompressible steady state CFD simulations and were not able to deliver valuable result in many cases. A goodexample of these limitations is highlighted by the study of the noise generated by a simple 'side mirror' shapewritten by R. Siegert [71]. Recent developments of this family of techniques require the use of transientsimulations and filtering to avoid loosing to much information on the coarser acoustic mesh. Reasonable successhas been met in specific areas involving low frequencies (up to a couple hundred Hz) and considerable CPU timeis needed.
An alternative methodology is to incorporate in a single numerical tool, right from the beginning, the ingredientsthat are necessary to perform direct Aero-Acoustic numerical simulation. They are:
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• Compressible Navier Stokes: To be able to propagate pressure waves and therefore take into account in a single simulation the flow and the noise, including all possible cavity modes. • Fluid structure coupling: To be able to treat the problems involving a turbulent flow on one side of the structure and the noise radiation on the other side. • Small time step: To be able to deal accurately with frequencies going up to several thousand Hertz. • Transient turbulence modeling: Unlike the Reynolds Averaged Navier Stokes (RANS) methods that makes the assumption that the flow is a combination of a steady state and turbulent fluctuations. Aero- Acoustic noise is directly linked to the small scale turbulence fluctuations and strongly time dependant. • Acoustic boundaries with prescribed impedance: This is a critical point of a good Aero-Acoustic simulation. Boundaries need to be able to perform tasks such as giving a free field impedance to an inlet with fixed velocity, prescribing a specific impedance at the outlet of a duct to make sure long wavelength stay trapped inside, treat exterior air impedance effect on a vibrating structure and be used to model absorbing materials (carpet, foams …) that are used to coat many components.These ingredients have been implemented in a single numerical code. The outcome is RADIOSS solver which isdifferent from the existing CFD codes in its capabilities and particularly well suited to short time transientanalysis.
∂ρMass + ((u − w ).∇ )ρ + ρ∇.u = 0 EQ. 126.96.36.199 ∂t
∂uMomentum ρ + ρ ((u − w ).∇ )u − ∇τ + ∇p = 0 EQ. 188.8.131.52 ∂t
∂ρeEnergy + ((u − w ).∇ )ρe + (ρe + p )∇.u = 0 EQ. 188.8.131.52 ∂tWhere u is the fluid velocity, w the grid velocity, ρ the density, p the pressure e the energy and τ the stresstensor.NOTE: In case of w=u, the system degenerates into the Lagrangian formulation, meanwhile w=0 describes the classical Eulerian formulation. Lagrangian formulation will be used for the structures when needed. An ALE fluid mesh is attached to the structure mesh, therefore able to undergo deformations tight to the structural vibrations.
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Acoustic phenomena are driven by pressure waves propagating in the materials. Those waves velocity, the soundspeed velocity c can be expressed by the following equations:
∂P c= ∂ρ EQ. 126.96.36.199
K c= EQ. 188.8.131.52 ρ
In the usual engineering fields, the sound speed is about 340 m/s for air and 1500 m/s for water.
Most of the CAA research in the industry is aimed at flow motions of relatively small Mach numbers.Therefore, CFD codes have widely used the incompressibility hypothesis which allows a fair simplification ofthe Navier Stokes equations. An incompressible flow is a flow for in which:
Dρ ∂ρ ⎛ ∂u ∂v ∂w ⎞ = + u.∇ρ << ρ ⎜⎜ + + ⎟ ⎟ EQ. 184.108.40.206 Dt ∂t ⎝ ∂x ∂y ∂z ⎠If this condition is fulfilled the mass conservation equation can be rewritten.
∇u = 0 EQ. 126.96.36.199
It has to be noted that an incompressible flow does not necessarily implies that ρ remains constant throughoutthe flow but that ρ remains constant along a streamline since one can substitute EQ.18.104.22.168 in EQ.220.127.116.11.Practically, this condition can be reasonably assumed for Mach numbers lower than 0.3 and in the case oftransient flows, if the time rate of velocity change is long compared to the time for a sound wave to traverse theflow field. Thus, the incompressibility hypothesis yields an instantaneous transmission of pressure waves in thefluid domain. Incompressible approach will not be able to simulate the propagation of acoustic waves nor thecavity modes tight to composition of reflected waves on a given geometry. It then becomes necessary to applyone of the following techniques: • Solve the compressible Navier Stokes equations to capture correctly the propagative nature of the noise waves. • Use additional equations to derive the noise sources from the flow field.Accordingly to the base criteria of always to the best solution for CAA, it has been decided to follow the firstpath that requires no specific assumptions and is physically and mathematically much better grounded. Bysolving the fully compressible Navier Stokes equations, it becomes possible to compute in a single simulationthe flow and the sound pressure wave's propagation. Since there is a large gap between the flow pressurevariations (in the order of hundreds of Pa in most cases) and the acoustic pressure variations (in the order of 1 Pa~94 dB), it has become critical to use 64 bits double precision arithmetic. Using 32 bits would yield flawedresults because the acoustic pressure levels would not be handled properly in many cases.The spatial integration of momentum equation is performed with a Finite Element integration using StreamlineUpwind Petrov Galerkin (SUPG) scheme [72], which was shown accurate enough to capture flow instabilities.Advection of state variables is achieved via a simple finite volume technique as in Donea's original paper [8].
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⎛ l ⎞ dt ≤ Min⎜⎜ ⎟ EQ. 220.127.116.11 ⎝ (c + u − w ) ⎟⎠where l is the characteristic element size, c the sound speed, u the flow velocity and w the grid velocity. Typicalvalues of dt for CAA applications are in 1 to 5 μ s range.
The choice of one formulation or the other will actually be dictated by the minimization of the CPU time for theconsidered application. Shall the goal be to simulate the defrosting of a windshield lasting about 5 minutes, withlow flow velocities, the several second time step allowed by the implicit scheme will be much more efficient. Inthe CAA case however, the frequencies of interest are going up to 5 to 10 kHz and the Nyquist criteria and antialiasing filtering imposes a sampling for the time domain recording of 20 to 40 kHz. Therefore, the maximumtime step that can be used in implicit will be 5x10-5s.The explicit time step being in the range of 2x10-6s, one hasto compare the cost of one implicit time step to 25 explicit time steps. A survey yield a ratio of about two ordersof magnitude between the CPU cost of both schemes in favor of the explicit and therefore, the explicit schemeCPU efficiency has been considered superior for CAA applications.
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In our case, since it has already been chosen to solve the transient Navier Stokes equations with an explicitscheme yielding a very small time step, the CFL condition does not imply any major constraint. Mesh sizecriteria have been developed in order to ensure a good CAA behavior and LES accuracy (also see ModelingMethodology in the next chapter).In noise generation zones where most of the turbulence is generated and small vortices are very active, the meshcriteria is:
⎛u ⎞ h < 0.1⎜⎜ ⎟⎟ EQ. 22.214.171.124 ⎝f ⎠Where h is the element size, u the flow velocity and f the highest frequency of interest. The last equation yieldsthe expression of local Reynolds number:
u.h ⎛ u2 ⎞ Re = < 0.1⎜⎜ ⎟⎟ EQ. 188.8.131.52 ν ⎝ f .ν ⎠Usually, u is in the 20 m/s range, f is 2500 Hz and the air viscosity ν =1.5x10-5m2/s. This yields a local Reynoldsnumber of 1000. A reinforced mesh criteria applied close to the walls is to have a y+ lower than 100. Although,these numbers might be considered as large by academic standards, it has been verified for various industrialapplications that the numerical predictions reasonably match the experimental data [73]. In the SGS model, thesub grid scale level energy dissipation ε SGS is proportional to the resolved scales stress tensor S ij and themodeled small scales stress tensor τ ij through a turbulent viscosity coefficient ν SGS .This turbulent viscosity is afunction of the filter width l (mesh size) and of the resolved scales (via the stress tensor).Cs is known as theSmagorinsky constant and has been experimentally evaluated to be 0.18 (this constant can be tuned for specificapplications and 0.1 is used by default in RADIOSS).
It has to be noted that an original pressure damping factor has been developed in order to better take into accountthe absorption of the acoustic waves on the boundary layers.
The elements neighboring the walls have a specific treatment depending upon the element size. A logarithmicvelocity profile is assumed in the first layer of elements and the corresponding modified viscosity is derived.
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The goal of boundary conditions is to replace the influence of the exterior of the computational domain by acondition that will let some frequencies go out and reflect others accordingly to the physical properties of thesurrounding materials. Acoustic impedance, defined by the ratio of the acoustic pressure ~p at a given locationover the acoustic velocity u n at the same location is a key notion.
~p Z= EQ. 220.127.116.11 un
ω k= EQ. 184.108.40.206 cwhere c is the sound speed. In the acoustic works, items are classically described as a function of the frequency.In particular, impedances describing the boundary conditions acoustic behavior. RADIOSS on the other hand isbased on a time domain description of the physical phenomena, it is therefore not possible to use directly thosedata and it is required to impose time dependant boundary conditions. For the non-reflective boundaryconditions, it has been decided to implement the linearized Euler equation by Bayliss and Turkell [74 ]:
∂ρ ∂u = ρc n + c ( p∞ − p ) EQ. 184.108.40.206 ∂t ∂t 2lc
Where n is the normal to the boundary surface and lc a relaxation factor toward the desired pressure p∞ .Practically, the last equation matches the radiation of a monopole situated at a distance 2 lc inside thecomputational domain.
• Duct noise: The noise radiated by a structural system of ducts whose vibrating walls are excited by a turbulent flow inside. Among the many examples, exhausts and Heat Ventilation and Air Conditioning (HVAC).
• Passenger perception of exterior wind noise transmitted by a side glass or plane cabin.
One might suggest that rather than using a complex FSI solution, a decoupled approach could be used. That isperforming a CFD (or pure fluid CAA) simulation on one hand and then apply to a structural model as aboundary condition the computed pressure field. Beyond the mere inconvenience tight to the external couplingof two numerical programs (flow and structure), this approach, which is reasonably grounded steady aeroelasticity phenomena and for low frequencies applications is not well suited to broad band CAA applications. Itis not practical to apply the transient pressure field with a sampling of 20 kHz on a fine mesh and even moreimportant, there is a dependency of the structure vibrations to the surrounding fluid impedances. This impedancecan be eventually modeled on the side where there is no flow but is extremely complex on the side exposed tothe turbulent airflow. Consequently, in most cases, a decoupled modeling will be flawed from the beginning.
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Accordingly to our goal of modeling all physical phenomena important for CAA, a full FSI has been developedbetween the well-established structural module of RADIOSS and the CFD/CAA module. Some specific optionshave been developed in order to make this interface practical among which: 1. ALE Subcycling. In most applications, there are 95% fluid elements and 5% or less structural elements. Unfortunately the sound speed is often one order of magnitude higher in the structure yielding a time step decreased by the same factor. The 5% structure element will impose to the 95% a time step 10 times smaller, which is obviously not desirable. A specific subcycling has been developed in order to compute the fluid elements with a decoupled time step from the structures. 2. Fluid – Structure interfaces have been developed to ease the mesh development. Those interfaces can be used to stitch arbitrary meshes together and can be used in either fixed or sliding mode (fluid-fluid fixed and sliding interfaces have also been developed to take care primarily of fan problems).
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2.4 ConclusionAlong the whole development process, the CAA orientation has been kept in mind for all the decisions and leadto the choice of the following methods: • Compressible 3D Navier stokes solver • Transient explicit time integration • LES Turbulence • Acoustic boundary conditions • Fluid Structure couplingThese ingredients are needed to perform CAA simulations with no particular assumptions on the flow (exceptedof course the use of a turbulence model), the fluid structures coupling or the vibrations, making RADIOSS afairly general code.
Further developments are considered among which we can cite the ability to deal with bent flows. On the realworld, in many interesting cases, the object to be studied is not positioned on a flat ground but embedded withina complex geometrical shape (for example a side mirror on a car).The flow, which hits the component, isdistorted by this geometry. Simulation of the whole vehicle with a CAA method is not practical beyond a fewhundred Hertz because of the huge number of elements needed in the propagation zone. Therefore, a methodmixing a steady state simulation of the far field to get proper bent boundary conditions and RADIOSS close tothe component and the acoustic sources zones is currently under development to perform CAA analysis of thiskind of problem well beyond 1000 Hz.
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with h the so-called smoothing length and W a kernel approximation such that:
Let a set of particles i=1, n at positions xi (i=1,n) with mass mi and density ρ i . The smoothed approximation ofthe function f is (summation over neighbouring particles and the particle i itself):
m ∏ f (x ) = ∑ ρ f (x )W (x − y, h) s i =1, n i i EQ. 126.96.36.199 i
∇f ( x ) = ∑ ρ f (x )∇W (x − y, h ) m i i EQ. 184.108.40.206 i =1, n i
The following kernel [83] which is an approximation of Gaussian kernel by cubic splines was chosen (Figure3.1.1):
3 ⎡ 2 ⎛ r ⎞ 2 1 ⎛ r ⎞3 ⎤ r ≤ h ⇒ W (r , h ) = ⎢ −⎜ ⎟ + ⎜ ⎟ ⎥ EQ. 220.127.116.11 2πh 3 ⎢⎣ 3 ⎝ h ⎠ 2 ⎝ h ⎠ ⎥⎦
3 1 ⎛ r⎞h ≤ r ≤ 2h ⇒ W (r , h ) = 3 ⎜ 2− ⎟ EQ. 188.8.131.52 4πh ⎝ h⎠
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This kernel has compact support, so that for each particle i, only the closest particles contribute toapproximations at i (this feature is computationally efficient). The accuracy of approximating EQ. 126.96.36.199 by EQ.18.104.22.168 depends on the order of the particles.
∫ W ( y − x, h) = 1, ∀x Ω EQ. 184.108.40.206
∫ ( y − x )W ( y − x, h) = 0, ∀x Ω EQ. 126.96.36.199
These equations insure that the integral approximation of a function f coincides with f for constant and linearfunctions of space.
[ ] Wˆ j ( x, h ) = W j (x, h )α ( x ) 1 + β (x ) • (x − x j ) , with W j (x, h ) = W (x − x j , h ) EQ. 184.108.40.206
where the parameters α x and() β (x ) are evaluated by enforcing the consistency condition, now given by thepoint wise integration as :
∑V Wˆ (x, h ) = 1, ∀x j j j EQ. 184.108.40.206
∑V (x − x )Wˆ (x, h ) = 0, ∀x j j j j EQ. 220.127.116.11
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These equations enable the explicit evaluation of the correction parameters α (x ) and β (x ) as follows:
−1 ⎡ ⎤ β ( x ) = ⎢∑ V j (x − x j ) ⊗(x − x j )W j ( x, h )⎥ ∑V (x j j − x )W j ( x, h ) EQ. 22.214.171.124 ⎣ j ⎦ j
1 α (x ) = [ ∑V jW j (x, h) 1 + β (x ) • (x − x j ) ] EQ. 22.214.171.124
Since the evaluation of gradients of corrected kernel (which are used for the SPH integration of continuumequations) becomes very expensive, corrected SPH limited to order 0 consistency has been introduced.Therefore, the kernel correction reduces to the following equations :
Wˆ j ( x, h ) = W j ( x, h )α ( x ) EQ. 18.104.22.168
∑V Wˆ (x, h ) = 1, ∀x j j j EQ. 18.104.22.168
1 that is α (x ) = EQ. 126.96.36.199 ∑V jW j (x, h) j
Note that SPH corrections generally insure a better representation even if the particles are not organized into ahexagonal compact net, especially close to the integration domain frontiers. SPH corrections also allow thesmoothing length h to values different to the net size Δx to be set.
⎛ di + d j ⎞ ⎡ ⎛ di + d j ⎞⎤W j (i ) = Wˆ ⎜⎜ xi − x j , ⎟⎟ and ∇W j (i ) = grad xi ⎢Wˆ ⎜⎜ x − x j , ⎟⎟⎥ if kernel correction, ⎝ 2 ⎠ ⎣⎢ ⎝ 2 ⎠⎦⎥ EQ. 126.96.36.199 ⎛ di + d j ⎞ ⎡ ⎛ d +dj ⎞⎤or W j (i ) = W ⎜⎜ xi − x j , ⎟⎟ and ∇W j (i ) = grad xi ⎢W ⎜⎜ x − x j , i ⎟⎟⎥ without kernel correction. ⎝ 2 ⎠ ⎣ ⎝ 2 ⎠⎦ EQ. 184.108.40.206At each time step, density is updated for each particle i, according to:
dρ = −ρi∇ ⋅ v i EQ. 22.214.171.124 dt i
∑ ρ (v − v j ) ⋅ ∇W j (i ) mjwith ∇ ⋅ v i = i EQ. 18.104.22.168 j
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Strain tensor is obtained by the same way when non pure hydrodynamic laws are used or in the other wordswhen law uses deviatoric terms of the strain tensor:
dvα β dx i m = ∑ j viα − vαj ρj dW j dx β ( ) (i ),α = 1...3, β = 1...3. EQ. 22.214.171.124
Next the constitutive law is integrated for each particle. Then Forces are computed according to :
mi dv [ ] = −∑ViV j pi ∇W j (i ) − p j ∇Wi ( j ) − ∑ mi m jπ ij [ ∇W j (i ) − ∇Wi ( j ) ] EQ. 22.214.171.124 dt i j j 2
where pi and p j are pressures at particles i and j, and π ij is a term for artificial viscosity. The expression ismore complex for non pure hydrodynamic laws. Note that the previous equation reduces to the following onewhen there is no kernel correction:
mi dv dt i [ ] = −∑ViV j pi + p j ∇W j (i ) − ∑ mi m jπ ij ∇W j (i ), since ∇Wi ( j ) = −∇W j (i ) EQ. 18.104.22.168 j j
d (d i ) ∇⋅v i = di EQ. 18.104.22.168 dt 3
in order particles to keep almost a constant number of neighbors into their kernels ( ρd is kept constant). 3
ci + c j − qb μij + qαμ ij2 π ij = 2 (ρ i + ρj) EQ. 18.104.22.168
d ij (vi − v j ) • (X i − X j ) with μ ij = 2 EQ. 18.104.22.168 Xi − X j + εd ij2
where X i (resp. X j ) indicates the position of particle I (resp.j) and ci (resp cj) is the sound speed at location i(resp.j), and qa and qb are constants. This leads us to introduce EQ. 22.214.171.124 and EQ. 220.127.116.11, as explained in [82].The artificial viscosity is decreased in regions where vorticity is high with respect to velocity divergence.
ci + c j − qb μij + qαμ ij2 π ij = 2 (ρ i + ρj) EQ. 126.96.36.199
20-jan-2009 29RADIOSS THEORY Version 10.0 SMOOTH PARTICLES HYDRODYNAMICS
d ij (vi − v j )• (X i − X j ) ( f i + f j ) ∇⋅v kwith μ ij = 2 , fk = EQ. 126.96.36.199 Xi − X j + εd ij2 2 ∇⋅v k + ∇×v k +ε′ ck dkDefault values for qa and qb are respectively set to 2 and 1.
⎛ ⎞Δt = Δtsca ⋅ min i ⎜ di ⎟, with α = ⎛⎜ qb + qa ⋅ μi ⋅ di ⎞⎟, and μi = max j (μij ) ⎝ i i i ( ⎜ c α + α 2 +1 ) ⎟ ⎠ i ⎜ ⎝ ci ⎟ ⎠ EQ. 220.127.116.11
Δt sca is the user defined coefficient (RADIOSS option /DT or /DT/SPHCEL). The value of Δt sca =0.3 isrecommended in [83].
2mi Δti = at particle i EQ. 188.8.131.52 Ki
⎛ di + d j ⎞ ⎡ ⎛ di + d j ⎞⎤W j (i ) = Wˆ ⎜⎜ xi − x j ′ ⎟⎟and ∇W j (i ) = grad xi ⎢Wˆ ⎜⎜ x − x j ′ ⎟⎟⎥ if kernel correction, ⎝ 2 ⎠ ⎣⎢ ⎝ 2 ⎠⎦⎥ EQ. 220.127.116.11
⎛ di + d j ⎞ ⎡ ⎛ d +dj ⎞⎤or W j (i ) = W ⎜⎜ xi − x j ′ ⎟⎟and ∇W j (i ) = grad xi ⎢W ⎜⎜ x − x j ′ i ⎟⎟⎥ if no kernel correction, ⎝ 2 ⎠ ⎣ ⎝ 2 ⎠⎦ EQ. 184.108.40.206Recalling that apart from the artificial viscosity terms:
[ Fi = ∑ Fij , Fij = ViV j pi ∇W j (i ) − p j ∇W j ( j ) ] EQ. 188.8.131.52 j
we write K ij = dFij d (ui − u j ) ≤ d d (ui − u j ) ( [ ViV j pi ∇W j (i ) + p j ∇Wi ( j ) ]) EQ. 22.214.171.124
20-jan-2009 30RADIOSS THEORY Version 10.0 SMOOTH PARTICLES HYDRODYNAMICS
where ui-uj is the relative displacement of particles i and j. Keeping the only first order terms leads to :
⎡ dpi dp j ⎤ K ij ≤ ViV j ⎢ ∇W j (i ) + ∇Wi ( j ) ⎥ ⎣⎢ d (ui − u j ) d (ui − u j ) EQ.22.214.171.124 ⎦⎥ dρi dρi ∇W j (i ) = ViV j i ⋅ ∇W j (i ) = ViV j ci2 ∇W j (i ) dpi dp d (ui − u j ) dρi d (ui − u j ) d (ui − u j )where ViV j
∇W j (i ) = mi ci2V&j2 ∇W j (i ) dpi 2
d (ui − u j )that is ViV j EQ.18.104.22.168
dp j ∇Wi ( j ) = m j c 2jV&i 2 ∇Wi ( j ) 2
d (ui − u j ) ViV j EQ.184.108.40.206
K i ≤ ∑ K ij EQ.220.127.116.11 j
2m j Wi ( j ) + W j (i ) Vi (smoothed ) = vi + α cs ∑ (v − vi ) EQ.18.104.22.168 ρi + ρ j j j 2
20-jan-2009 31RADIOSS THEORY Version 10.0 SMOOTH PARTICLES HYDRODYNAMICS
h03 mp ≈ ρ EQ.18.104.22.168 2since the space can be partitioned into polyhedras surrounding each particle of the net, each one with a volume :
h03 Vp ≈ EQ.126.96.36.199 2
ρVBut, due to discretization error at the frontiers of the domain, mass consistency better corresponds to mP = nwhere V is the total volume of the domain and n the number of particles distributed in the domain.
Figure 3.7.1 Local view of hexagonal compact net and perspective view of cubic centered faces net
Note that choosing h0 for the smoothing length insures naturally consistency up to order 1 if the previousequation is satisfied.Weight functions vanish at distance 2h where h is the smoothing length. In an hexagonal compact net with sizeh0, each particle has exactly 54 neighbors within the distance 2 h0 (Table 3.7.1).
h0 12 12
2h0 6 18
3h0 24 42
2h0 12 54
5h0 24 78
20-jan-2009 32RADIOSS THEORY Version 10.0 SMOOTH PARTICLES HYDRODYNAMICS
mp ≈ c3ρ EQ.126.96.36.199
By experience, a larger number of neighbors must be taken into account w.r.t. the hexagonal compact net, inorder to solve the tension instability as explained in following sections. A value of the smoothing length between1.25c and 1.5c seems to be suitable. In the case of smoothing length h=1.5c, each particle has 98 neighborswithin the distance 2h.
c 6 6
2c 12 18
3c 8 26
2c 6 32
5c 24 56
6c 24 80
2 2c 12 92
3c 6 98
20-jan-2009 33


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